Objective 1: Performance Measures for Identifying ... · Arterial Performance Measures Working...

NCHRP Project 3-79a Arterial Performance Measures

Working Paper No. O1-1

Objective 1: Performance Measures for Identifying Operational Improvement

Opportunities at a Signalized Intersection

Prepared for: National Cooperative Highway Research Program

Transportation Research Board National Research Council

Transportation Research Board

NAS-NRC LIMITED USE DOCUMENT

This report is furnished only for review by members of the NCHRP project panel and is

regarded as fully privileged. Dissemination of information included herein must be approved by the NCHRP.

Prepared by:

Chris Day and Darcy Bullock

Purdue University

May 31, 2009

NCHRP Project 3-79a: Arterial Performance Measures

May 31, 2009 Purdue University

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Objective 1: Performance Measures for Identifying Operational Improvement Opportunities at a Signalized Intersection

Contents

Abstract ....................................................................................................................... 2

Introduction .................................................................................................................. 3

Basis for Performance Measures................................................................................. 3

Reducing Signal Event Log Data into Performance Measures .................................... 4

Details of Performance Measure Calculation ............................................................... 6

Cycle Length ............................................................................................................ 6

Phase Green Time ................................................................................................... 8

Percentage Occurrence of Pedestrian Phase Calls ................................................. 9

Vehicle Counts ....................................................................................................... 10

Equivalent Hourly Flow Rate .................................................................................. 11

Volume to Capacity Ratio ....................................................................................... 12

Distribution of Phase Termination Codes ............................................................... 14

Percent of Vehicles Arriving on Green ................................................................... 15

Arrival Type ............................................................................................................ 17

Delay ...................................................................................................................... 18

Delay Estimated by Input-Output Queue Polygon Method ..................................... 18

HCM Estimated Delay ............................................................................................ 22

Degree of Intersection Saturation........................................................................... 26

References ................................................................................................................ 29



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Abstract

Objective 1 of NCHRP 3-79A is to define performance measures for a single intersection. This working paper discusses the details of calculating performance measures using event-based logged data at a signalized intersection. These measures are envisioned as the intersection-level components of a drill-down dashboard performance measure reporting system. The performance measures presented here are adapted from the Highway Capacity Manual (HCM) methodology using quantities that are typically used as inputs to the HCM delay equation. Cycle length, phase effective green time, vehicle counts, and equivalent hourly flow rates of vehicle counts are basic measures reflecting cycle events. The volume-to-capacity ratio is a measure that identifies phase capacity utilization and can be used to detect phase failures. Progression quality is characterized by measuring the proportion of vehicles arriving on green, which is used to calculate arrival type. The degree of intersection saturation is calculated to characterize overall intersection capacity utilization. Methods of estimating delay are also discussed.



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Introduction

Performance measures are emerging as an important tool for transportation agencies to allocate resources and to provide feedback on the effectiveness of resource allocation. Figure 1 shows an example of a high level dashboard, with limited drill-down capability in the area of interstate performance (Figure 2). As computing and communication technology continues to improve, we can envision a system of this sort eventually being able to interface with infrastructure such as traffic signal systems. Objective 1 of 3-79b is to define traffic signal system performance measures and is particularly timely in light of the 2007 Traffic Signal Report Card (1) that gave the industry a grade of “F” in the area of traffic monitoring (Figure 3). We believe that improving the area of traffic monitoring and performance measures will yield two complementary products that are urgently needed:

1. Enhanced quantitative data for making operational decisions on the maintenance of split, cycle, offset, and plan change times.

2. A formal systematic process of documenting system performance so that decision makers understand where investments can be made, and then observing a measurable impact of that investment.

In addition to supporting traffic operations engineers’ day-to-day operation of traffic signal systems, we envision that these performance measures would be incorporated into the drill down functionality of an agency dashboard (Figure 1). The goal of this white paper is to define the analytical framework that relies on existing traffic signal infrastructure (perhaps with an upgraded controller and upgraded loop detector amplifiers) that measures the performance of an isolated traffic signal. These performance measures are ultimately intended for practical use by operations engineers. A subsequent white paper will discuss techniques for viewing these performance measures at the network level.

Basis for Performance Measures

Elements that have for several years represented standard technology in general computing, such as Ethernet connections and IP addressed devices, are available in newer traffic control devices. Now is an appropriate time to reassess practices for evaluating signal system performance. There are opportunities to do so within present field detector infrastructure and using accepted traffic engineering models. The Highway Capacity Manual (HCM) (2) represents the result of over a half century of research into the capacity of roadways. While the authors do not necessarily believe that the HCM represents the best framework for designing signal settings, it contains many measures that characterize signal operation. Many of these appear as inputs to the HCM delay equation1,

( ) 321 ddPFdd ++= , Equation 1

1 d2 and d3 not shown in this section for sake of brevity.



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( )

−

−

=

C

gX

C

gC

di

i

i

,1min1

15.0

2

1 , Equation 2

where: d = control delay (s/veh) d1 = uniform delay (s/veh), PF = progression factor, d2 = incremental delay (s/veh), d3 = initial queue delay (s/veh), C = cycle length (s), Xi = volume-to-capacity ratio of phase i, and gi = green time for phase i (s). Rather than using traffic volumes, green time, and cycle length to estimate delay by this set of equations, the approach presented here develops performance measure reports based on the inputs to this equation. The uniform delay (Equation 2) and progression factor (PF) represent the simplest term in the HCM delay equation, and from these we can build the following phase-level performance measure concepts:

• Capacity utilization. The volume-to-capacity (v/c) ratio (Xi) is an important component of the delay equation, influencing d1 and d2. This measure qualitatively assesses whether a phase has extra green time that could be reallocated to other phases (Xi < 1.0), or whether the phase is near (Xi ~ 1.0) or over capacity (Xi > 1.0).

• Quality of Progression. The progression factor (PF) is used to adjust the d1 term to correct for platoon arrival characteristics. While PF suffers from limitations (3), it is calculated using the percentage of vehicles arriving on green (POG), which is a fundamental piece of information about the quality of progression. From POG, other measures such as the arrival type (AT) may be derived.

The remainder of this document will define procedures for going from logged data to performance measures and then the details of the performance measure calculations.

Reducing Signal Event Log Data into Performance Measures

High-resolution traffic signal status information (phase and detectors) is essential for developing performance measures. For the data sets used to illustrate these examples, an Econolite ASC/3 controller was used (5). This unit has a built in data logger that allows the archived data to be retrieved using the FTP protocol (Figure 4).



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Although a specific vendors equipment was selected, the data could be easily gathered by alternate means. For example, past data collection activities supporting NCHRP projects 3-79 and 3-66 were carried out using the data logging capability of industrial I/O devices (4) and field data input ports available on video detection systems (5, 6, 7, 8, 9). Additional alternatives include data acquisition cards (10) and other proprietary systems (11). The signal events of interest for this paper consisted of:

• Vehicle Phase Events. Four time stamped phase events are obtained from the data logger: start of phase green, start of phase yellow, start of phase red clearance, and end of phase. The end of phase time marked the end of the red clearance interval and the beginning of the next phase green.

• Vehicle Detector On/Off States. Two types of events, detector “on” and detector “off” events, were recorded. The timestamp of each detector actuation and release was recorded for detectors on each approach of the test intersection.

• Phase Termination Codes. At the end of green for each phase, the reason for phase termination was logged. The three typical reasons for phase termination were gap out, force off, and max out.

• Pedestrian Phase Events. Three events related to pedestrian phases were logged: beginning of ped walk phase, ped clearance phase (flashing don’t walk), and end of pedestrian clear phase.

• Pedestrian Calls. Timestamps were collected indicating when the pedestrian button was actuated.

• Plan Transition Times. At each timing plan pattern change, the cycle length and splits were recorded. A changeover between patterns was described by ten events: the new pattern, new cycle length, and splits for the eight phases in use.

• Coordinator Status. The coordination mode was reported as its status changed. Coordinator states included record of transition modes (adding, subtracting, dwell), a record when local zero was passed, and records reflecting when coordination began and when the signal was released to free mode.

Each logged event consisted of three items:

• A timestamp containing the date and time of the event, with resolution of 0.1 second. This is the smallest division of time used by the signal controller.

• A number representing event type (phase green, phase yellow, detector on, detector off, etc.).

• A number representing the event channel. For phase information, this was the number of the phase for which the event was relevant, and for detector information the number corresponded to the detector channel number.

Figure 5 shows the flow of data through the performance measure extraction process. This is a high-level view that hides the computational details, but it does show the five major components of the procedure.



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• First, the raw data are extracted from the log file and stored in tables corresponding to the event type. Phase event types and detector event types are separated.

• Steps 2 and 3 can be done simultaneously as they both create independent views of the data. When steps 2 and 3 are complete, we will have a table of cycles and a table of phase instances.

o In step 2, cycle length is measured by going through the phase events and discovering when cycle boundaries take place. This will be explained momentarily.

o In step 3, the numbers of vehicles counted during each instance of each phase are recorded.

• Step 4 is to aggregate these tables to extract phase-level performance measures by combining information obtained in the cycle table (cycle length) with information in the phase tables (green time and counts). The following section describes the computation of these performance measures in detail.

• Finally, in step 5, cycle-level performance measures are calculated. These are performance measures that take data from multiple phases as input. The degree of intersection saturation is the only cycle-level performance measure discussed in this paper.

Beyond this, the data could be further aggregated across intersections to produce system-level performance measures. This is shown in step 6. This will be the topic of a subsequent white paper.

Details of Performance Measure Calculation

Cycle Length

Cycle length is an essential component of most of the performance measures discussed in the remainder of the document, and the beginning of cycle time is used as the points in time for which all the other performance measures are referenced. Cycle length is normally a property of coordinated operation. However, if we define a cycle as the amount of time that it takes for all phases for which there are calls to be served, then it is also possible to define cycles for non-coordinated operation. Figure 6(a) shows a ring diagram representing operation of a typical eight-phase, dual-ring controller. To more precisely define a cycle length, we generalize the ring diagram by breaking into four pieces as shown in Figure 6(b). The barriers (thick vertical lines) divide phases into two blocks. Each block defines compatible phases: any phase can run at the same time as another phase in the same block, as long as it is not in the same ring. We define a cycle as the time between successive transitions from block 1 to block 2, or whenever Barrier 2 is crossed. Figure 7(a) illustrates this in more detail. This figure shows a controller progressing through phases in a typical manner for a coordinated signal. The barriers are shown as defined in Figure 6(b) by the progression of phases. The cycle length delineated in this figure begins when Barrier 2 is crossed and ends at the next time that this event takes place. The reason why Barrier 2 is chosen and not Barrier 1 is that



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phases 2 and 6 are the coordinated phases. Thus, the end of green for phases 2 and 6 represents a repeating point in the cycle. During free operation, phases 2 and 6 typically are representative of the major phases and are appropriate to use for measuring the provided cycle length when no fixed cycle length is set by the controller. Figure 7(b) shows an example of cycle length calculation during free, or low-volume coordinated operation. This shows an example of a case where there is low demand for phases 3, 4, 7, and 8, and the controller cycles through phases 1, 2, 5, and 6 for an extended time. In this case, we continue to measure cycle length whenever there is a transition from Block 1 to Block 2.

Figure 8 shows a 24 hour plot of cycle length at the test intersection (SR 37 & 32, Noblesville, IN). The line shows a 20-point running average, and the vertical lines represent TOD plan change times. The signal runs coordinated from 0600 to 2200, and free from 2200 to 0600. The cycle length varies quite significantly during the free periods, representing times of day in which there was very little demand for the minor phases, and the controller typically rested in green for phases 2 and 6 for long intervals.

The fixed cycle length of the coordinated periods is apparent in this graph. Each of the six coordinated plans between 0600 and 2200 tend to have a plateau that represents a cycle length. Some plan transitions reflect changing splits while the cycle length stays roughly the same. There is a little variance in the measured cycle length because this signal runs actuated coordinated phases (7). After passing the yield point, coordinated phases 2 and 6 are allowed to gap out before the end of cycle, leading to some cycles with shorter cycle lengths. The “loss” of time in one cycle is made up by the subsequent cycle being slightly longer. The yield points are not allowed to drift, which preserves the offsets and keeps coordination in step. When actuated coordinated phases are used in conjunction with fixed force-offs, minor phases benefit from being given additional green time. Note that during the peak hours (0600-0900, 1500-1900), fewer points stray from the average line, indicating that the coord phases have held on to all of their green time and not gapped out. Table 1 shows an example calculation of cycle length. Table 1(a) contains a table of times when the controller phase on/off states changed. The timestamp in the third column represents the beginning of the time period in which the signal operated in this state. For example, at time 13:22:48.1, phases 2 and 5 became green; at 13:23:09.5, these phases finished their red clearance time and phases 3 and 7 became green; and so on. Between 13:22:48.1 and 13:23:09.5, the controller served phases in Block 1; then, from 13:23:09.5 to 13:24:11.5, the controller served phases in Block 2, etc. The second column from the right shows when a transition from Block 1 to Block 2 was detected by processing the phase signal states. This represents the crossing of Barrier 2 as defined in Figure 6 and defines the boundary between cycles. The rightmost column shows the count of cycles starting from midnight. Table 1(b) illustrates how these times are used to calculate cycle lengths. In Table 1(a), we detected a cycle boundary at 13:25:03.9 and the next one at 13:26:47.9. This corresponds to the third row of Table 1(b). The cycle length is 104.0 seconds. This represents the 556th measured cycle during the day of November 12, 2008.



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Phase Green Time

The next item that can be observed from phase information is the amount of green time that is allocated to each phase during a cycle. Figure 9(a) illustrates how this is calculated from logged events. The phase green event (tG) marks the time period when the green indication was given to the phase. The phase yellow (tY) and phase red (tR) events mark the transition into yellow and then into the all red clearance period. Finally, the phase off (tOFF) event marks the transition from red clearance into the green indication of the next phase (or, alternately, an exclusive pedestrian phase or an interval where no phase was served, as might occur during preemption or if the signal rests in red). The phase split is measured by taking the difference tOFF – tG. Yellow and red clearance times can be measured from phase events or known a priori from signal settings. The green time is equal to the split time less the total clearance time (yellow plus red). The effective green time represents the amount of green time that is utilized by vehicles. This concept is illustrated by Figure 9(b), which provides the HCM definition of effective green (2). The equation for effective green is:

elgg ispliti +−= 1, Equation 3

Where: gi = the effective green of phase i (s), gsplit = the measured length of the observed split (s), l1 = the start-up lost time (s), and e = the amount of the clearance interval used by vehicles (s). The HCM suggests the values l1 = 2 s, and e = 2 s, but notes that during congested conditions e could be longer than 2 s. In this paper, we have used the HCM suggested values, but note that the appropriate values may need to be fine-tuned to reflect driving conditions at a particular location, or to conform with agency practices. Figure 10 shows a 24-hour plot of green time for phase 4 on November 12, 2008 at SR 37 & 32 in Noblesville, IN. The x-axis point on which any of the points is plotted is the beginning of the cycle in which the phase takes place. Force off points are observable during the coordinated period, such as the cluster where the circled point sits (around 1330). This represents when phase 4 reached its force off point, a common occurrence because this is a busy phase. Points above this line represent when phase 4 received additional green time as a result of prior phase gap outs or omits. Points below the line reveal when phase 4 gapped out. During the overnight free periods (2200-0600), we can observe many points at 8 s, representing where one or two vehicles arrived and were served by the min green time. Cycles when phase 4 was omitted (0 s) are also visible. Table 2 presents details on the calculation of green time. The highlighted row corresponds to the circled point in Figure 10. Here, the beginning of green took place at 13:25:18.5 and the phase ended at 13:26:00.1. Subtracting the time out gives a total split time of 41.6 s. It is known from the signal settings2 that the yellow time is 3.9 s and

2 The clearance times may also be measured from the raw data.



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the all-red clearance time is 2.0 s, which gives a total clearance time of 5.9 s. Subtracting that from the split yields a green time of 35.7 s. The beginning of green time at 13:25:18.5 is matched to the beginning cycle time of 13:25:03.9. That is the time value used for plotting the point in Figure 10.

Figure 11 shows 24-hour plots of green time for eight phases at SR 37 & SR 32 in Noblesville, IN. The placement of the eight phases in the diagram is representative of the location of these phases in the ring diagram for that intersection. That is, phase 5 (northbound left turn) lags phase 6 (southbound through). From this graph it is apparent that the coordinated phases 2 and 6 tend to receive the most green time, especially during the peak periods, which is what we would expect as these are the most important movements. The crossing through movements (4 and 8) receive a somewhat smaller amount of green time. The left turn phases receive much less time, with the exception of phase 5, which is a heavy movement.

Percentage Occurrence of Pedestrian Phase Calls

While this document focuses on vehicle performance measures, pedestrian service is extremely important at many locations. Some past research has been carried out at the test intersection of Northwestern and Stadium in West Lafayette, IN (12). In this paper, we present the most basic measurement of pedestrian service, which is the prevalence of pedestrian calls (ped button actuations). Figure 12 shows the percentage of vehicle phases with calls for the adjacent pedestrian phase at this intersection for two consecutive Wednesdays representing one week before classes and the first week of classes at Purdue University. The difference in pedestrian activity between the two periods can be clearly seen in the figure. The percentage of phases with pedestrian calls is given by:

ipedinoped

iped

pp

p

,,

, Phases Ped Percent

+= Equation 4

where: pped,i = the number of phase instances with pedestrian phases, and pnoped,i = the number of phase instances with no pedestrian phase. Besides showing daily and seasonal variation in pedestrian activity, such charts reveal equipment problems such as a stuck or nonfunctioning pedestrian button. Because the pedestrian phase effectively creates a minimum duration for the adjacent vehicle phase, pedestrian activity must be taken into account when considering changes to signal settings.



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Vehicle Counts

Previous sections have discussed quantifying how a signal controller partitions time into cycles and phases, and when special phases (such as pedestrian phases) are called. It is also important to quantify demand. One measurement to describe demand would be the number of vehicles counted during a cycle for each phase. To collect vehicle counts, pulse detectors are required for each movement lane group. Often, intersections feature only presence detectors; however, count (pulse) detectors are becoming more common (11). It is important to distinguish between loop detector presence and count output. In Figure 13, the side view of a lane with a stop bar detector is shown. The exact size and configuration of the stop bar detector can vary considerably, but typically they encompass a 50 ft zone comprised of either one long loop, two or more quadrupole loops, or four 6x6 ft loops wired in series. For this example, we suppose that the detector provides an input to a detector card that simultaneously measures presence and vehicle counts. At t = t0, no vehicle is yet in the detection zone, and the detector is off. At t = t1, the first vehicle enters the detection zone and the presence trace turns on. At the same time, the count trace registers a pulse. At t = t2, the first vehicle is in the middle of the detection zone and the presence state remains on. At t = t3, the first vehicle has nearly exited the detection zone, but the front of the second vehicle has just entered it. The count detector is able to register the entry of the second vehicle with a second pulse, but there is no evidence of it in the presence trace. Only when the detection zone is free of vehicles (t = t4) does the presence trace fall to a low state. Using the presence state will give us the detector occupancy, but using count pulses allows us to directly measure the number of vehicles served. Figure 14 shows examples of loop detector cards available from three manufacturers that are capable of producing count output. Video detection systems are able to provide similar information, but perhaps with less accuracy. Figure 15 illustrates how vehicle counts are assigned to a phase instance and thereafter mapped to a cycle. The top three rows define blocks and cycles as in Figure 6. The fourth row shows the phase 4 green state. An adjustment is made to account for the vehicle utilization of clearance time (the quantity e in Equation 3). Counting intervals are defined by the end of green plus e. The counts on lanes assigned to phase 4 are shown beneath as dots plotted along a timeline. Vehicles counted during the red indication of a phase are associated with the following green phase. The reason for this is that these vehicles are unable to move through the intersection until they receive the green indication. For example, for cycle n, if were to base the vehicle count on the cycle boundaries, we would count 6 vehicles. However, this would have assigned the 3 vehicles counted in the preceding red phase to cycle n – 1, although they could not have passed through the intersection until cycle n. By using the counting interval for phase 4 in cycle n, the proper number of vehicles is counted; 8 vehicles were served by phase 4 in cycle n, and 6 vehicles were served by phase 4 in cycle n + 1. For protected-permitted left turn (PLT) phases, additional logic must be applied. Because the phase green time for protected-permitted phases includes only the time that the green arrow indication is shown, we do not count vehicles during the permitted portion of the phase since they do not move during the protected green time.



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Figure 16 illustrates the logic for determining whether a count was a permitted left turn. The first row in this figure shows the indication for phase 7. The green, yellow, and red times for phase 7 are associated with the protected phase and represent changing indications for the left turn arrow lenses in the signal head. Phase 7 does not show a red ball, but the phase state is “off”. For part of that time, phase 7 left turns are permitted while the adjacent phase (phase 4) has the green indication. When phase 4 turns off, a red ball is shown for both phases 4 and 7. Vehicles arriving for a phase are considered to move in the protected phase when:

• Phase 7 is on (vehicles move past stop line on green)

• All phases in Block 2 are off (vehicles arrive at stop line during red phase and cannot move until next time Phase 7 is green)

The trace of this logic state is shown in the fifth row (“PLT logic”). Vehicle A is a

protected left turn since it occurs during the phase 7 green arrow, and is thus counted. Vehicle B is a permitted left turn since it takes place while phase 7 is dark and phase 4 is green. We do not count vehicle B for phase 7. Finally, Vehicle C takes place while the intersection is serving phases in block 1. We do count Vehicle C since it will be served in the following green phase3. Figure 17 shows a 24 hour plot of counts for phase 4 on Wednesday, November 12, 2008 at SR 37 and SR 32 in Noblesville, IN. The graph illustrates the high variance of counts from cycle to cycle, and it also shows the trend by time of day. Clearly, Phase 4 is busier during the PM peak hour than any other time of day. Table 3 illustrates how counts are tabulated. The shaded row in the table corresponds to the circled point in Figure 17. The two concurrent ends of green that define the counting interval are 13:24:05.7 and 13:25:54.2. The value of e used here is 2.0 seconds, which adjusts the cutoff points to 13:24:07.7 and 13:25:56.2. A total of 21 vehicles were counted within this interval. This instance of phase 4 is associated with the cycle beginning at 13:25:03.9. Figure 18 shows counts for all eight phases at the Noblesville test intersection. The directional characteristics of the northbound (phase 2) and southbound (phase 6) movements are clearly visible. The counterpart to eastbound phase 4’s PM peak can be seen in westbound phase 8’s AM peak.

Equivalent Hourly Flow Rate

Count graphs are useful, but because cycle lengths may change by time of day, counts are not necessarily comparable over time. Consider the difference between 21 vehicles counted in 60 seconds versus 21 vehicles counted during 120 seconds. To normalize the values, the raw counts may be converted into the equivalent hourly flow rate. By dividing the number of counts by the cycle length, we obtain a rate of vehicles per second, which can be converted into vehicles per hour. The result is the equivalent hourly flow rate of the individual counts:

3 We acknowledge that this is an approximation of phase demand. Later tasks in this project will examine

the use of both the protected demand and detector occupancy at the end of both the permitted and protected phases to evaluate the probability of a split failure.



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3600×=C

NV i

i Equation 5

Here, Vi is the equivalent hourly flow rate for phase i, Ni is the number of vehicle counts for phase i, C is cycle length, and 3600 converts units from vehicles per second to vehicles per hour. Figure 19 shows a 24 hour plot of the equivalent hourly flow rate for phase 4 on Wednesday, November 12, 2008 at the Noblesville test intersection. The plot is very similar to the 24-hour count plot in Figure 17. However, apart from the difference in scale, the vertical positions of points in Figure 17 are different from those in Figure 19 because each has been normalized to the cycle length. In Figure 17 there are many cycles between midnight and 0600 where 1 to 4 vehicles were served. When normalized (Figure 19), the numbers translate into a much wider range of flow rates because cycle length has a very high variance at this time (Figure 8). Table 4 shows examples of how the cycle length is calculated. The shaded row corresponds to the circled point in Figure 19. In Table 3, we observed that 21 vehicles were counted for phase 4 during this cycle. The cycle length is 104 s. Dividing 21 by 104 s yields a flow rate of 0.2 vehicles per second. We multiply this by 3600 to obtain the equivalent flow rate of 727 vehicles per hour. Figure 20 shows plots of equivalent hourly flow rate for all eight phases at the Noblesville test intersection.

Volume to Capacity Ratio

So far, the plots that we have presented have been measurements of what occurs at the signal. The example plots illustrate how green time is assigned and how many vehicles are being served. However, these measurements do not tell whether there is too little or too much green time for any particular phase. In order to assess the utilization of green time, we calculate the volume-to-capacity (v/c) ratio, given by the HCM equation 16-7 (2):

ii

i

i

ii

i

i

igs

CV

C

gs

V

c

vX =

=

= ,

Equation 6

Where: Xi = the v/c ratio for phase i, Vi = the flow rate for phase i (veh/h), si = the saturation flow rate for phase i (veh/h), gi = the effective green time for phase i (s), and C = cycle length (s).



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We can simplify Equation 6 by substituting Equation 5 for Vi, which causes the cycle length to be canceled out of the equation.

i

i

ii

ig

N

sc

VX

3600=

= , Equation 7

Where: Ni = the vehicle count for phase i, si = the saturation flow rate for phase i (veh/h), and gi = the effective green time for phase i (s). Figure 21 shows a 24-hour plot of v/c ratio for phase 4 at the Noblesville test intersection. The plot shows the stochastic variation in v/c ratio from cycle to cycle, a consequence of the variance in the number of vehicles. The horizontal red line marks the v/c = 1.0 line. Above this line are values of v/c where the observed equivalent hourly flow rate exceeds the saturation flow rate. Table 5 gives an example of V/C Ratio calculations; the shaded row corresponds to the circled point in Figure 21. For phase 4 during the cycle beginning at 13:25:03.9, 21 vehicles were counted and a green time of 35.7 was measured. Assuming a saturation flow rate of 1900 veh/h, we apply Equation 7 and obtain v/c = 3600 × 21 / (1900 × 35.7) = 1.115. Alternately, we can calculate the v/c ratio by directly dividing volume with capacity. The capacity (as defined by the HCM) is calculated from the following equation:

C

gsc i

ii = , Equation 8

Where: ci = the capacity of phase i, si = the saturation flow rate for phase i (veh/h), gi = the effective green time for phase i (s), and C = cycle length (s). For the example phase described above, the cycle length is 104 seconds. The capacity is 1900 × 35.7 / 104 = 652 veh/h. From Table 4, we know that the equivalent hourly flow rate is 727 veh/h. From these, we can calculate the v/c ratio: 727 / 652 = 1.115. Figure 22 shows V/C Ratio for 8 phases at SR 37 and SR 32 in Noblesville, IN. The peaking patterns tend to follow the volume graphs in Figure 20. However, the differences between Figure 20 and Figure 22 show that looking at volumes alone does not give any information about capacity utilization. For example, in Figure 20, the volumes for phases 4 and 8 look similar. However, in Figure 22 we can see that phase 4 runs close to capacity for many cycles, in stark contrast to phase 8, where virtually all of the v/c points are less than 0.5. This is because phase 8 has two lanes and phase 4



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has one. Phase 8 has twice as much capacity, so its v/c ratios are about half that of phase 4. A split failure is typically defined as when the phase green time is not long enough time to serve the demand. The higher the value of the v/c ratio, the more likely it is that a split failure has occurred. For convenience, we select v/c = 1 as the point at which to consider where a split failure happens4. Figure 23 shows a 24-hour plot of the count of split failures for the eight phases at the test intersection. For example, the two short bars with a height of 2 and 1 in the phase 2 box correspond to the three dots in two different 30 minute intervals that exceed 1.0. Based upon quick visual inspection of these graphs, it is clear that phases 3 and 5 have capacity problems. The other phases do see occasional split failures but they are not as common. Notably, the coordinated phases (2 and 6) see very few split failures outside of their peak hours. The v/c ratio and the associated analysis of capacity utilization depends on the value of saturation flow rate that is selected. In this paper, we have used 1900 veh/h/ln in all cases, but this value may not be appropriate for all locations and for the same location under different conditions. Thus, the selection of the saturation flow rate should be carried out with some care to improve the accuracy of the measurements that use it. The effect of changing local conditions on intersection capacity is the subject of current NCHRP project 3-97.

Distribution of Phase Termination Codes

Phase termination codes document why the controller ended a phase. There are three typical termination codes:

• Max Out: the phase is terminated because it has reached the programmed maximum green time and there is a call for another phase.

• Force Off: the phase is terminated because it has reached its force off point during coordinated operation.

• Gap Out: the phase is terminated because it has exceeded its gap time, and there is a call for another phase.

• Omit: in addition to termination codes, phases are omitted when there is no call for them and they are skipped. No code is given for a phase omit, but it becomes apparent when matching phase instances to cycles when omits occur.

Figure 24 shows stacked bar graphs showing the percentage of cycles in each half hour where phases gapped out, forced off, maxed out, or were omitted. No phases were observed to max out; during the coordinated periods, the force off points are reached long before the green time reaches maximum green, and during the free periods there was not enough traffic to hold a phase long enough to cause a max-out. Phases 2 and 6 are never omitted because the intersection is set to soft recall to these phases. Phases 2 and 6 are allowed to gap out during the coordinated part of the day because they are actuated coordinated phases, as discussed earlier.

4We expect to more precisely characterize this probabilistic relationship in subsequent tasks.



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For some phases, the proportion of force-offs roughly corresponds to the degree of capacity utilization shown in Figure 22. For example, phase 6 forces off almost 100% of the time during the AM peak period, which corresponds to the high v/c ratios for phase 6 (Figure 22). Phase 1 is omitted much of the time, and it usually gaps out when it is served. Phase 7 has a similar chart. Phases 3, 4, and 5 force off recurrently during the peak periods. Phases 4 and 8 appear to force off with roughly the same frequency. However, recall from Figure 22 that phase 8 v/c ratios were well below saturation because phase 8 has two lanes. The rather high frequency of force-offs is explainable by the fact that vehicles on this approach tend to use the right lane more than the left lane. As a consequence, overall flow rates are well below capacity, but the steady stream of vehicles in the right lane prevents the phase from gapping out.

Percent of Vehicles Arriving on Green

Volume-to-capacity ratio and phase termination codes give us information on how the green time for phases is utilized. However, these measures do not impart any information on the quality of progression along the coordinated arterial. The basic measure of progression quality is the percentage of vehicles arriving during the green indication. For this measure, vehicle counts at advance detectors (typically set back 250–400’ in advance of the stop bar) are used. Stop bar counts are not suitable because once they are occupied by the first vehicle, it is impossible to characterize the arrival of subsequent vehicles. Typically, advance are only available on coordinated phases, because agencies install them to provide dilemma zone or volume-density operation during non-coordinated periods. Figure 25 shows how the proportion of vehicle arriving on green (POG) is calculated. Here, phase 2 is the phase of interest. Combining the on/off state of the phase with known yellow and red times yields the green time (Figure 9). Vehicles that are detected during the preceding red indication are counted as arrivals on red; vehicles detected during the green indication are arrivals on green. Vehicles that are detected at the advance detectors after the beginning of the yellow phases are unlikely to clear the intersection and are therefore counted as arrivals on red for the next cycle. An optional adjustment, ε, can be added to the clearance time to calibrate the model. This will be discussed in more detail later. The equation for POGi of phase i is:

iGiR

iG

iiNN

NPPOG

,,

,

+== , Equation 9

where NG,i is the number of arrivals on green for phase i and NR,i is the number of arrivals on red for phase i. In Figure 25, we would count 0 red and 2 green arrivals for cycle n (P2 = 1); 3 red and 5 green arrivals for cycle n + 1 (P2 = 0.63); and 3 red and 4 green arrivals for cycle n + 2 (P2 = 0.57). Figure 26 shows a 24-hour plot of POG for phase 2 on November 12, 2008 at SR 37 and SR 32 in Noblesville, IN. Table 6 shows example calculations of POG; the



16

highlighted row corresponds to the circled point in Figure 26. Three of the columns in this table are timestamps.

• Vehicles counted between the Last End of Green (with an optional adjustment) and the Beginning of Green are counted as arrivals on red.

• Vehicles counted between the Beginning of Green and End of Green (with an optional adjustment) are counted as arrivals on green.

The cutoff point between when an arrival takes place on red or green is a potential source of inaccuracy in calculating POG. The location of the advance detectors, vehicle speeds, and the preference of drivers to stop or to proceed when they see the yellow indication are all factors that can affect what the appropriate cutoff point would be. Sharma (13) examined the behavioral process in detail. The adjustment factor ε is used to capture these effects. In this paper, we have used ε = 0, but at some locations it may be appropriate to use a different value. Figure 27 shows a schematic of phase events and potential values for ε that would adjust the end of green time to produce a particular cutoff point. For example, if ε = 2, it changes the adjustment factor shown in Figure 25 to Y + AR – 2, pushing the cutoff point forward by two seconds. This implies that most vehicles passing by the detector will proceed through the intersection up to 2 seconds into yellow. Figure 28 shows 20-point moving averages of POG calculated using different values of ε. While the shapes of the curves are significantly impacted by the selection of ε, this plot shows that there is room to enhance the accuracy of POG by fine tuning the cutoff point. Arrivals on red and green can also be shown graphically. For each vehicle arrival, we can find the time in the cycle where it is detected. Likewise, we can do the same for the beginning of green and end of phase times. If we plot each of these events by time in cycle over time of day, we produce a plot that looks like Figure 29. This plot, here referred to as a Purdue Progression Diagram (PPD), graphically shows the events in Table 6, as well as the individual vehicle arrivals (black diamonds). The x-axis represents the zero of time in cycle, or the beginning of cycle. The green phase begins at approximately 56 seconds (shown by the green line) and ends at approximately 99 seconds (shown by the blue dashed line); the phase and the cycle both end at 104 seconds (shown by the black line). Here, we see that there are 4 vehicles arriving in the red phase and 9 in the green phase (there are a few overlapping points in the figure), leading to a POG of 0.692. Figure 30 shows a Purdue Progression Diagram extended to 24 hours. Figure 29 represents a magnified view of one cycle in Figure 30. The green line represents the beginning of the phase and the black line represents the end of the cycle, which is also the end of green for phase 2. The plot compares agrees with the graph of POG shown earlier in Figure 26. Overall, the majority of vehicles arriving at this phase arrive during the green phase (between the green and black lines in Figure 30). The northbound platoon is very easy to see during the AM peak hour (Figure 30, area A). During the PM peak hour, there is considerably more demand for this movement and the platoon is denser (Figure 30, area B); sometimes the platoon extends beyond the end of green the next cycle (Figure 30, area D). We can also see the influx of vehicles that are not



17

part of the main platoon; these are fed into the approach from turns into the northbound direction at upstream intersections (Figure 30, area C). A similar plot for the northbound movement at the upstream signalized intersection at SR 37 and Pleasant St is shown in Figure 31. The corresponding plot of POG is juxtaposed to the image to show how the visual dispersion of arrivals in the bottom plot compares to the measured POG. In this plot, it is apparent that the primary coordinated platoon is being cut off by the end of green between 1300 and 1500 (Figure 31, area A). Also, the secondary platoon coming from minor, non-coordinated phases at the upstream intersection (Figure 31, area B) can be more clearly seen here than in the previous figure.

Arrival Type

Arrival Type (AT) is a qualitative measure of progression quality; arrival types are rated from 1 to 6 based on the platoon ratio, Rp. Rp is based on POG, but is adjusted by the ratio of green time to cycle length (g/C):

i

ii

iip POG

g

C

C

g

POGR ==, ,

Equation 10

Where: Rp,i = the platoon ratio for phase i C = cycle length (s), gi = green time for phase i (s), and POGi = the proportion of vehicles arriving on green. Table 7 shows how AT scales to Rp. This table is taken from HCM Exhibit 15-4 (2), with the exception of the rightmost column, which shows an piecewise interpolation of the integer AT values on Rp. A graph of this interpolation is shown in Figure 32. The reason for carrying out the interpolation is to make use of the qualitative scale of AT, which is widely used in the HCM methodology and software packages such as HCS-

2000 and SYNCHRO, whereas Rp might be less familiar. Interpolated AT ≥ 4 represent favorable progression; < 3 represent unfavorable progression; and between 3 and 4 are representative of random arrivals (neither favorable nor unfavorable progression). Figure 33 shows a 24-hour plot of AT for phase 2 at the Noblesville test intersection on November 12, 2008. Overall, we can see that the AT tends to be above 4 for the majority of cycles, indicating that the quality of progression is better than random arrivals for the most part. Table 8 shows example calculations of AT, with the shaded row corresponding to the circled point in Figure 33. For the cycle beginning at 13:25:03.9, phase 2 had a POG of 0.692; phase 2 green time was 41.8 s out of a cycle length of 104.0 s, meaning that g/C = 41.8/104.0 = 0.402. Dividing POG by g/C, we obtain Rp = 1.72. Referring to Table 7, we see that this Rp value corresponds to AT 5, and yields an interpolated AT value of 5.44.



18

The effect of adjusting for the g/C ratio can be seen from the first two rows of data in Table 8. Cycle 554 and 555 have similar POG values. However, the g/C ratio for cycle 554 is about twice as large as that of cycle 555. Cycle 555 is assigned a higher value of Rp (and therefore AT) because it was able to achieve the same POG with a smaller share of green time. The arriving platoon might have been very similar for both phases, but since cycle 554 used much more green time (relative to the cycle length), its value of AT is substantially lower.

Delay

Delay is an important performance measure because it is directly experienced by drivers. Control delay is the primary source of variance in arterial travel times. Delay is the basis for the HCM level of service (LOS) for signalized intersections, and continues to serve as a critical performance measures for many traffic engineers. All delay estimation methods are accompanied by some limitations. The objective of this paper is to identify performance measures that can be calculated with relative ease, rather than to improve existing estimation methods. In the following sections, we have applied the following two methodologies to analyze real-time data:

• Input-Output delay (14, 15) uses vehicle arrival information to construct an arrival profile. A constant departure profile is assumed to build a queue polygon. The area of the polygon is equivalent to the total delay incurred in the cycle, which is divided among the vehicles to produce the average delay.

• HCM (2) delay estimation is widely used in the traffic engineering profession to make operational decisions using 15 minute flow rates. When analysis periods are reduced below 15 minutes and movements become saturated, the robustness of this model deteriorates.

Delay Estimated by Input-Output Queue Polygon Method

Methodology

Previous work by Sharma et al. (14, 15) conducted as a part of NCHRP 3-79 investigated methods of estimating delay using real-time vehicle counts. Two methods were developed:

• The input-output method used vehicle arrivals at the advance detector to build an arrival profile, and assumed a continuous departure profile to construct the queue polygon.

• The hybrid method also used vehicle arrivals at the advance detector to build an arrival profile, and used stop bar count detection to build a departure profile to construct the queue polygon.



19

In this paper, we present only the input-output method as it is somewhat simpler and more applicable for practitioners (few intersections have both advance and stop bar loops on an approach). Additionally, Sharma et al. (14) found that the additional information used in the hybrid method did not lead to an improvement in the quality of the delay estimation. Figure 34 shows an example of a queue polygon constructed using a vehicle arrival profile and departure profile. Figure 34(a) shows an arrival profile created using actuations of the advance detector, and Figure 34(b) shows a departure profile using a continuous function to approximate a departure curve made of discrete vehicle departures. Figure 34(c) shows the queue polygon that results from subtracting the departure curve from the arrival curve. Phase events shown here represent the last end of green (LEOG), beginning of green (BOG), and end of green (EOG). Vehicle arrivals at the advance detector are projected forward to the time when they would arrive at the stop bar. The departure profile begins at BOG + δ, where δ is an adjustment for start-up lost time. The slope of the departure profile (Figure 34(b)) assumes that traffic will flow at the saturation flow rate after BOG + δ. Mathematically, the resulting queue polygon represents the difference between the two functions (Figure 34(a), Figure 34(b)). The area under the curve represents the total delay. This quantity can be calculated in real time by breaking the polygon into intervals at each vehicle arrival. For the ith vehicle, interval delay is calculated by looking back at the previous interval [ti–1, ti] and applying the appropriate formula. The beginning of queue discharge at BOG + δ and EOG also set boundaries for the intervals. During the red phase, the increase in total delay depends entirely on the arrival profile. The delay is given by a rectangular area as shown in Figure 35(a). The delay associated with this interval is given by

( )11 −− −= iiii ttvd , Equation 11

where: vi–1 is the number of vehicles in the system at ti–1, ti is the arrival time of the ith vehicle, and ti–1 is the arrival time of the (i–1)th vehicle. One subtle note worth highlighting is that vi–1 is used in Equation 11 instead of vi because the ith vehicle has only just arrived and has not yet accrued any control delay. During an interval in the green phase, the delay monotonically decreases with time. When all of the vehicles discharge from the system, a triangular delay area is created as shown in Figure 35(b). The amount of delay for this interval is given by

( )1121

−− −= iDii ttvd , Equation 12

where tD is the time when all vehicles present in the system at time ti–1 are expected to discharge, which is equal to:

svtt iiD /11 −− += , Equation 13



20

where s is the saturation flow rate in vehicles per second. When tD ≤ ti, all vehicles should be able to discharge assuming that they proceed at the saturation flow rate. However, if tD ≥ ti, there is not enough time for all of the vehicles to discharge. In this case, a trapezoidal queue polygon area is created as in Figure 35(c). The amount of delay accrued during an interval such as this is given by

( )( ) ( )11121

−−− −+−−= iirriiii ttvvvttd , Equation 14

where vr is the number of residual vehicles, the formula for which is

,1 iir cvv −= − Equation 15

where ci is the interval capacity,

( )1−−= iii ttsc Equation 16

This represents the number of vehicles that should have departed the intersection during the interval assuming that they do so at the saturation flow rate s. The minimum value for vr is zero, which is achieved when tD = ti or vi–1 = ci and the entire queue is discharged. Negative values are not valid and would indicate a calculation error. Note that Equation 14 simplifies to

( )( )121

−−+= iirii ttvcd , Equation 17

which is ideal for computation but unhelpful when explaining the origin of the formula. Finally, the total delay during a cycle is found by summing the delay for all intervals; the average delay is then computed by dividing the total delay by the total number of vehicles served by the phase. If there were residual vehicles left at the end of the ending interval, these would be added to the next cycle. For the first interval in the next cycle, vi–1 = vr. Figure 36 shows a 24 hour plot of input-output delay for Phase 2 at the test intersection on November 12, 2008. A moving average line is provided to show the average conditions throughout the day, although the variance is quite high; delay values spread over a range of 30s at all hours of the day. The high delay values in the early morning periods represent cycles where a single vehicle might have waited for ~45 s to receive the green indication. During busier times of day, the impact of long delays that vehicles arriving on red experience are mitigated by the vehicles that arrive on green, reducing the average delay. Phase 2 delay is heaviest during the PM peak hour, which is not surprising since this is when the demand for this movement peaks. Table 9 shows a detailed calculation of the input-output delay for the circled point in Figure 36. The first row shows that there were 2 residual vehicles left from the previous cycle. The rest of the rows in the table represent the intervals for which delay is calculated for the cycle of interest. The second row is the first interval, which ends at the vehicle arrival taking place at t1 = 17:30:45.9. The previous event was the last end of green, which happened at t0 = 17:30:45.0. The phase is currently red, so the queue is



21

not discharging. The interval width is t1 – t0 = 0.9 s. There are two vehicles in the system at t0 (i.e., v0 = 2), so the total delay d1 is equal to v0 × (t1 – t0) = 2 × 0.9 = 1.8 s per Equation 11. The delay is calculated using the number of vehicles at 17:30:45.0. Because the vehicle arriving at 17:30:45.9 has only just arrived, it has not yet contributed to the delay. Finally, we increment the number of vehicles at the end of the interval so that v1 = 2 + 1 = 3. The next vehicle arrives at t2 = 17:30:47.1, which is the end of interval 2. The interval width is t2 – t1 = 1.2 seconds. There were three vehicles in the system (v1 = 3) at t1 = 17:30:45.9. Again, the phase is red, so we obtain a rectangular interval delay equal to v1 × (t2 – t1) = 3 × 1.2 = 3.6. This is added to the 1.8 s of delay accrued during interval 1, so total delay becomes 5.4 s. Lastly, v2 = 3 + 1 = 4. The first interval after the beginning of green is i = 16. Queue discharge is taking place during this interval. There are 16 vehicles in the system at the beginning of the interval (v15 = 16). The interval width is t16 – t15 = 6.4 s, which leads to an interval capacity of (6.4 s) × (1.056 veh/s) = 6.8 veh. Because this is not enough time to clear all 16 vehicles in the system, there are 16 – 6.8 = 9.2 residual vehicles remaining. To these vehicles, the most recent vehicle arrival is added, so that v16 = 9.2 + 1 = 10.2. The delay incurred during the 16th interval is given by Equation 17: d16 = (t16 – t15)(0.5c16 – vr) = (6.4)[0.5(6.8) + 9.2] = 80.8 s. Interval 19 is the first where the queue completely discharged. In this case, the interval capacity c19 was equal to the number of vehicles in the system (v18 = 6.4). The triangular delay area was calculated using Equation 12: d19 = 0.5 × 6.4 × 6.8 = 21.9 s. As for the remaining intervals, once the queue has fully discharged, no further delay is accrued. The 26th interval represents a situation where two vehicles were detected at the same time (t26 = t25). This is possible because there are two lanes on this approach. Although this causes a residual vehicle to be observed, no delay is accrued. Finally, at the end of green (i = 27), the total delay of 1066.6 s accrued during the cycle is divided among the 27 vehicles detected during the cycle. The average delay is calculated to be 39.5 s/veh.

Limitations

Input-output delay uses information from one location, the position of the advance detectors. The assumption is made that vehicles have not begun to decelerate until after they have crossed this point. Thus, this method deteriorates during oversaturated conditions where queues reach the advance detectors. The departure of vehicles is approximated by a uniform departure profile that includes an amount of start-up lost time. Residual queues are carried over from one cycle to the next, thus increasing the size of the queue polygon, but no additional provision is made for overflow delay. The computed average delay applies to both residual vehicles at the beginning of the cycle and to all vehicles arriving during the cycle. For example, in Table 9, the two vehicles carried over from the previous cycle have already been delayed by a certain amount. However, that delay was included in the total delay of the previous cycle, and for purpose of making the calculation practical, the delay counter is reset to zero at each end of green so that the delay due to residual vehicles is distributed proportionally to each cycle.



22

HCM Estimated Delay

Methodology

In this section, we demonstrate the application of the HCM methodology to the volumes and green times that we previously measured from real-time data. It demonstrates that it would be possible to rapidly input data collected in real time to existing models, provided the assumptions behind the delay equations are not violated. The HCM definitions of LOS grades are given in Table 10. The HCM equation for estimating delay is

( ) 321 ddPFdd ++= , Equation 18

where: d1 = uniform delay (s/veh), PF = progression factor, d2 = incremental delay (s/veh), and d3 = initial queue delay (s/veh). It is important to note that we have excluded initial queue delay d3 from this analysis due to the imprecision with which many of the necessary parameters can be measured or estimated. Therefore, delay estimated by the example shown here might be underestimated in cases where initial queue delay is significant. Uniform delay d1 for phase i is given by:

( )

−

−

=

C

gX

C

gC

di

i

i

,1min1

15.0

2

1 , Equation 19

where: C = cycle length (s), Xi = volume-to-capacity ratio of phase i, and gi = green time for phase i (s). The progression factor PF for phase i is given by:

PA

i

f

C

g

POGPF

−

−=

1

1,

Equation 20

where: POG = proportion of vehicles arriving on green, gi = green time for phase i (s),



23

C = cycle length (s), and fPA = supplemental adjustment factor for platoon arriving during green. In this analysis, we have set this factor equal to the HCM default values for simplicity. Incremental delay d2 is given by:

( ) ( )

+−+−=

Tc

kIXXXTd

i

iii

811900

2

2 , Equation 21

where: T = duration of analysis period (h), Xi = volume-to-capacity ratio of phase i, k = incremental delay factor, dependent on controller settings, I = upstream filtering/metering adjustment factor, here taken to be equal to 1, and ci = capacity of phase i (veh/h). During a typical paper-based HCM field study, T = 0.25 (15 minutes) would be a typical value to be used in the d2 formula. The sensitivity of d2 to the selection of a value for T is shown in Figure 37. At values of Xi representing unsaturated conditions, incremental delay is minor regardless of what value is used for T. When Xi enters the saturated regime, incremental delay increases with T, implying that the longer that a high Xi is sustained, the more incremental delay accumulates. The incremental delay factor k is given by:

( )( )5.0

,5.021

min

minmin

≤≤

+−−=

kk

kXkk i. Equation 22

Values for kmin depend on vehicle unit extension. These values are shown in Table 11. Figure 38 shows a 24-hour plot of HCM estimated delay for 15-minute intervals using the data set from November 12, 2008. The circled point is for the 13:30–13:45 interval, which includes the example calculations used in much of the rest of this paper. delay reaches its maximum during the PM peak, which is also when volume peaks for this movement. There is an interesting spike in delay at 0500. During this hour, flow rates are starting to increase, but the signal still runs free. Cycle lengths are increasing due to increased vehicle activity, and more phase 2 vehicles are arriving on red. Lower values of POG and g/C ratio result, which cause a higher delay to be calculated. Apart from this spike, delay seems to be most strongly influenced by the volume. Qualitatively, delay appears to be acceptable, with LOS “C” or better. Details of the calculation are shown in Table 12. The average cycle in the 13:30–13:45 time period had a cycle length of 104 seconds, and phase 2 was given a green time of 39.2 s on average. From this we calculate a g/C ratio of 0.377. There were 74 vehicles arriving on green out of 144 total vehicles, therefore POG = 0.514. Using the 144 total vehicles in Equation 7 gives X2 = 0.402. Entering that into Equation 19 gives d1 = 23.8 s/veh. Equation 20 gives PF = 0.780. Because the analysis period is 15 minutes, T = 0.25 h; the vehicle extension is 2.4 s, so kmin = 0.08. from Equation 22, we



24

calculate k = 0.08. From Equation 8 we obtain capacity c = 1433 veh/h. Equation 21 gives d2 = 0.1 s/veh. Finally, we calculate the total delay by Equation 18, assuming d3 = 0: d = d1(PF) + d2 = 23.8(0.780) + 0.1 = 18.7 s/veh.

Calculating HCM Delay Using 5-minute Analysis Intervals

It was demonstrated that 15-minute HCM delay can be calculated from real-time data. Smaller analysis intervals can also be used. Figure 39 shows a 24-hour plot of HCM estimated delay based on 5-minute intervals. A 12-point (60 minute) moving average is shown by the black line. Example calculations are shown in Table 13. The 15 minute interval from 13:30–13:45 shown in Table 12 corresponds to the three five-minute intervals beginning at 13:30, 13:35, and 13:40 in Table 13. Generally, the 5-minute delay plot in Figure 39 follows the same trend as the 15-minute curve in Figure 38. Delay reaches a maximum during the PM peak hour; the peak appears to come somewhat earlier. There is considerably more variance in the 5-minute plot, and the range of values has expanded to include one point in the LOS “D” region. That high point was lost in the 15-minute delay, which essentially took the average of that 5-minute interval and two others. Since the calculation for 5 minute intervals are analogous to the 15 minute intervals, we have not included detailed text describing Table 13. We would point out that the total delay calculated from the three intervals beginning at 13:30, 13:35, and 13:40 is extremely close to the delay calculated by the 15 minute interval beginning at 13:30 in Table 12. Total delay is equal to the HCM delay multiplied by the number of vehicles. Thus, the total 15 minute delay for the 13:30 interval is 18.7 × 144 = 2692.8 s. The sum of the three 5-minute intervals’ total delay is 51(21.1) + 43(16.3) + 50(18.3) = 2692 s. The minute difference is likely due to rounding error in these calculations. This is what we would expect, especially since the uniform delay term (d1×PF) is dominant in the total delay. We will show later that as we reduce the analysis period, the incremental delay term gives different results.

Calculating HCM Delay on a Cycle-by-Cycle Basis

Next, we demonstrate the possibility of performing this calculation on a cycle-by-cycle basis. However, because the intention of the HCM methodology is to analyze 15-minute count data, a cycle-by-cycle analysis extends the HCM methodology beyond its design intent. While it is possible to use the cycle boundaries to define analysis periods, this invalidates some portions of the HCM methodology that rely upon interactions spanning multiple cycles. Also, because delay is related to cycle length and v/c ratio, the results of the measure are questionable when cycle lengths vary, as during free operation (Figure 8, 2200-0600). Figure 40 shows a 24-hour plot of HCM estimated delay for phase 2 at SR 37 & SR 32 in Noblesville, IN on November 12, 2008. Table 14 shows example calculations of HCM delay; the shaded row, showing the same cycle that we have looked at in the previous tables, corresponds to the circled point in Figure 40. Generally, the shape of the plot is very similar to the 5-minute interval HCM delay plot in Figure 39. There is more variance in the cycle-by-cycle plot, and more points in the LOS “D” region.



25

For the cycle beginning at 13:25:03.9, based on C = 104 s, g2 = 41.8, and X2 = 0.317, uniform delay d1 = 21.3 s/veh by Equation 19. From POG = 0.692, we find that PF = 0.514 using Equation 20. To find incremental delay d2, first a value of k must be found. For a vehicle extension of 2.4 s, kmin = 0.08. Combining this with X2 in Equation 22 gives k = (1 – 2 × 0.08)(0.317 – 0.5) + 0.08 = –0.07. However, this is less than kmin, so k = kmin = 0.08. The analysis period, T, is in this case equal to the cycle length, so T = C = 104 s = 0.029 h. It is assumed that I = 1. Capacity c2 = 1527 veh/h, from Equation 8. Entering these values into Equation 21 returns d2 = 0.1 s/veh. The total HCM estimated delay is equal to d1 (PF) + d2 = 11.1 s/veh (Equation 18).

Comparison of 15-minute, 5-minute, and Cycle-by-Cycle Delay

Figure 41(a) shows superimposed plots of HCM estimated delay from 15-minute, 5-minute, and cycle-by-cycle analysis periods. Figure 41(b) shows the cumulative total delay from the three 24-hour series of HCM delay estimates. The overall trend in the three delay estimates are quite similar. The curves experience peaks and troughs at very similar times of day as seen in Figure 41(a). The cumulative total delay curves shown in Figure 41(b) track each other very closely until approximately 1700. If we break apart the delay into the uniform (d1×PF) and incremental (d2) terms, the reason for the divergence of the three estimates becomes clear. Figure 42(a) shows a plot of d1(PF) and d2 as separate data sets, with 20 point moving averages for each series. A moving average of the total delay is also shown. The incremental delay d2 is negligible until the PM peak hour, which is when the three curves diverge in Figure 41(b). This is also the only time of day when v/c ratios approach or exceed 1.0. In Figure 42(b), the cumulative amounts of total delay attributable to the uniform (d1×PF, upper plot) and incremental (d2, lower plot) delay terms are shown for 15-minute, 5-minute, and cycle-by-cycle analysis periods. Note the difference in vertical scale on the two plots. The uniform delay for all three analysis period types are very close, with cycle-by-cycle delay producing slightly higher uniform delay. This is because cycle boundaries do not coincide with 5-minute or 15-minute interval boundaries. The incremental delay clearly shows a dependence on the length of the analysis period. Nearly twice as much incremental delay is calculated when we move from 15-minute intervals to 5-minute intervals. Cycle-by-cycle calculations give us three times as much incremental delay as 15-minute intervals. As shown in Figure 37, incremental delay is highly sensitive to Xi as well as to T. Reducing T has a multiplicative effect on incremental delay (Equation 21). However, higher values of Xi become available to input into the equation that are lost in the averages when longer analysis periods are used. It would seem that the effect of having higher Xi values wins out against the smaller T values.

Comparison of Cycle-by-Cycle HCM Estimated Delay to Input-Output Delay

Noting that the two delay estimates are defined differently, and that estimating delay by the HCM method on a cycle-by-cycle exhibits problems in the saturation regime, we compare cycle-by-cycle HCM delay with input-output (IO) delay to show the similarity in the trends for the two delay estimates, and to highlight the differences. Figure 43(a) shows superimposed 20 point moving averages of the two delay



26

estimations. The two lines are well correlated, with the strongest peaking occurring around 18:00 and with many smaller peaks taking place at the same time. Figure 43(b) shows a scatter plot of HCM delay versus input-output delay, showing that the two measures do correlate reasonably well (R2 = 0.75), although there is a great deal of variance leading to many points quite far from the regression line. Some of the variance is due to the different ways in which vehicles are counted for input-output delay and for the v/c ratio calculation. Some descriptive statistics accompanying this figure are given in Table 15. The HCM delay tended to be slightly higher on average during peak hours, while input-output delay was higher during off-peaks. The input-output delay had more variance except during the AM peak. The input-output delay is affected by the actual distribution of vehicle arrivals as they appear in real time, whereas the HCM delay uses PF to take this into consideration. Using PF thus eliminates some of the variance due to the randomness of the vehicle arrival pattern. Some limitations of using PF are discussed further by Gartner and Deshpande (3) in a recent paper.

To conclude, this paper has tabulated HCM estimated delay for intervals shorter than the intended 15-minute intervals. However, we have also shown that the length of the analysis period has an impact on the amount of delay estimated. While in general the estimates were close, they diverged during congested conditions. We would recommend that readers use caution in implementing HCM delay estimation for analysis periods shorter than 15 minutes, and consider using methods such as the Input-Output method for estimation of delay on a cycle-by-cycle basis.

Degree of Intersection Saturation

The degree of intersection saturation (XC), also called the critical volume-to-capacity ratio, is a measure described in the HCM. The equation for XC is (2):

−

=∑

LC

C

s

VX

i ci

C , Equation 23

where: C = cycle length (s), L = lost time (s), and ∑(v/s)ci =the summation over critical phases ci of the ratio of volume (V) to saturation flow rate (s). This measure describes how much of total signal capacity is being used, based on the volumes of movements in the critical path. The critical path is the series of phases that carry the highest volumes. In an operating scheme where multiple sets of phases run concurrently, the set with the highest volume is “critical.” For a dual-ring, eight-phase controller, there are four possible critical paths, as shown in Figure 44. We compare phases {1,2} against {5,6} and {3,4} against {7,8} because the boundary between phases within a pair is allowed to move independently from the other pair, while both pairs simultaneously end at a barrier. Going back to the terminology of rings



27

and blocks used earlier in the paper, each block has one ring where the critical phases lie. For a dual-ring eight-phase controller, Equation 23 simplifies to (16):

−

+

=

LC

C

s

v

s

v

s

v

s

vXC

78345612 ,max,max , Equation 24

Where, for example, v12/s = v1/s + v2/s. Figure 45 shows a 24-hour plot of Xc for SR 37 & 32 at Noblesville, IN for November 12, 2008. The symbols in the plot correspond to the critical path during each cycle. From the figure it is clear that phases {5,6,3,4} dominate for most of the day, with {1,2,3,4} becoming dominant in the PM peak hour. The distribution of XC values represents an aggregation of the 8 phase volumes in Figure 20. As XC approaches 1, the intersection is increasingly more congested, and there are fewer seconds of underutilized green time that could be redistributed to address capacity problems. Example calculations of XC are broken down into three tables. Table 16 shows the calculation of volume-to-saturation (v/s) ratios and the determination of critical path in block 1. Table 17 shows these items for block 2. The final steps in the calculation of XC are shown in Table 18. The highlighted rows in these tables correspond to the circled point in Figure 20. Starting from Table 16, for the cycle beginning at 13:25:03.9, the v/s ratio is computed for phases {1,2} (Ring 1, Block 1) in Table 16(a). Phase 1 was omitted, so it has zero volume and therefore v1/s1 = 0. Phase 2 has a volume of 485 veh/h. Using with a saturation flow of 3800 veh/h gives v2/s2 = 0.128. The total lost time is 6.0 s, representing the lost time associated with phase 2. We do not include lost time for phase 1 since it was omitted. The saturation flow rate associated with Ring 1 Block 1 is (v/s)R1B1 = (v/s)12 = v1/s1 + v2/s2 = 0 + 0.128 = 0.128. The v/s ratio associated with phases {5,6} (Ring 2, Block 1) is found similarly in Table 16(b). (v/s)R2B1 = (v/s)56 = v5/s5 + v6/s6 = 0.109 + 0.155 = 0.264. In Table 16(c), the two v/s values are combined to determine the critical path. Here, (v/s)12 < (v/s)56, so the critical path for block 1 is 56, and the v/s ratio for Block 1, (v/s)B1, is equal to 0.264, with an associated lost time LB1 = 12.0 s. Table 17 repeats the comparison for block 2. Table 17(a) shows the calculation of v/s for phases {3,4} (Block 2, Ring 1), and Table 17(b) shows the calculation of v/s for phases {7,8} (Block 2, Ring 2). The v/s ratios for the two parts are (v/s)R1B2 = (v/s)34 = 0.474 and (v/s)R2B2 = (v/s)78 = 0.091. In Table 17(c), we compare the two v/s ratios and find that the critical path is 34, the v/s for block 2 is (v/s)B2 = 0.474, and the lost time for block 2 is 11.1 s. We bring information from the critical paths and v/s ratios from the two blocks together in Table 18 to calculate XC. The two v/s ratios are summed: (v/s)B1 + (v/s)B2 = 0.264 + 0.474 = 0.738, which represents ∑(v/s)ci in Equation 23. The lost times for each block are also added up to produce the C/(C–L) correction factor. Here, L = 23.1, C = 104.0, giving C/(C–L) = 1.286; multiplying this by 0.738 (the sum of v/s ratios) gives XC = 0.949. When combined with information about split failures, XC can be used to assist in making decisions about signal timing. Figure 46 shows a plot of XC including only points where split failures have taken place. Different symbols represent the different phases here, and overlapping symbols indicate where multiple phases experience split failures.



28

The 20-point running average of XC is shown for all cycles, including those without split failures. Phases 3 and 5 have the most obvious problems here, which is expected since these phases saw the largest numbers of split failures in Figure 23. For most cycles, XC is below 1.0, implying that there is some underutilized green time that could be reallocated to address persistent split problems. The lower XC is, the more of this underutilized green time there should be, so whereas during the peak hours there may be only fractions of a second to move around, during the off-peak there may be enough time to make a noticeable impact on the operation of a failing phase.

Conclusion

This paper presented a number of performance measures that can be calculated using data logged in real-time at a signalized intersection. These included direct measurements of events at the intersection such as vehicle counts and controller assignment of green time. Performance measures supporting operational decisions included volume-to-capacity ratio for analysis of capacity utilization and arrival type for evaluation of progression quality on the coordinated phases. Ultimately, the end products for these performance measures could be used:

• As components of reports for traffic engineers on which to base decisions for making operational changes to splits, cycle lengths, offsets, and other parameters.

• As instruments of evaluating operational changes in before/after studies, providing feedback to the engineer on the impact of signal timing adjustments.

The benefits of developing a set of reliable performance measures include better targeting of resources, thus promoting institutional efficiency. Additionally, decreasing the lead time on feedback from making operational changes will also improve understanding of the system by its operators and open the path to improved management of traffic signal systems by substantiating the experience of the traffic engineer with valid evidence.



29

References

1. 2007 National Traffic Signal Report Card Technical Report. National Transportation Operations Coalition, Washington, DC, 2007.

2. Highway Capacity Manual. TRB, National Research Council, Washington, DC, 2000.

3. Gartner, N.H. and R. Deshpande. “Assessing Quality of Progression with Cyclic Coordination Factors.” Proceedings of the 88th Annual Meeting of the Transportation Research Board, Washington, DC, January 11-15, 2009.

4. Grenard, J., D. Bullock, and A. Tarko, Evaluation of Selected Video Detection Systems at Signalized Intersections, Joint Transportation Research Program, Report FHWA/IN/JTRP-2001/22, West Lafayette, IN: Purdue University, 2001.

5. Smaglik, E.J., A. Sharma, D.M. Bullock, J.R. Sturdevant, and G. Duncan, “Event-Based Data Collection for Generating Actuated Controller Performance Measures.” Transportation Research Record No. 2035, Washington, DC: Transportation Research Board, pp. 97–106, 2007.

6. Smaglik, E.J., D.M. Bullock, and A. Sharma, “A Pilot Study on Real-Time Calculation of Arrival Type for Assessment of Arterial Performance,” ASCE Journal of Transportation Engineering, Vol. 133, No. 7, pp. 415-22, July 2007.

7. Day, C. M., E.J. Smaglik, D.M. Bullock, and J.R. Sturdevant. ”Quantitative Evaluation of Actuated Versus Nonactuated Coordinated Phases,” Transportation Research Record No. 2080, Washington, DC: Transportation Research Board, pp. 8–21, 2008.

8. Bullock, D.M., C.M. Day, J.R. Sturdevant, ”Signalized Intersection Performance Measures for Operations Decision Making,” ITE Journal, August 2008.

9. Day, C.M., E.J. Smaglik, D.M. Bullock, and J.R. Sturdevant, Real-Time Arterial Traffic Signal Performance Measures, Joint Transportation Research Program, Report FHWA/IN/JTRP-2008/9, West Lafayette, IN: Purdue University, 2008.

10. Liu, H.X. and W. Ma, “Real-Time Performance Measure System for Arterial Traffic Signals,” Transportation Research Record, Paper ID: 08-2503, 2007.

11. “Using Existing Loops at Signalized Intersections for Traffic Counts: An ITE Informational Report,” ITE Journal, Vol: 78, Issue: 2, February 2008.

12. Hubbard, S.M.L., D.M. Bullock, and C. M. Day, “Opportunities to Leverage Existing Infrastructure To Integrate Real-Time Pedestrian Performance Measures Into Traffic Signal System Infrastructure,” Transportation Research Record No. 2080, Washington, DC: Transportation Research Board, pp. 37–47, 2008.

13. Sharma, A., “Integrated Behavioral and Economic Framework for Improving Dilemma Zone Protection Systems,” PhD Dissertation, Purdue University, August 2008.

14. Sharma, A., D.M. Bullock, and J. Bonneson, “Input-Output and Hybrid Techniques for Real-Time Prediction of Delay and Maximum Queue Length at a



30

Signalized Intersection," Transportation Research Record, #2035, TRB, National Research Council, Washington, DC, pp. 88-96, 2007.

15. Sharma, A., and D.M. Bullock, “Field Evaluation of Alternative Real-Time Methods for Estimating Delay at Signalized Intersections,” Proceedings of the 10th International Conference on Applications of Advanced Technologies in Transportation, Athens, Greece, May 27-31, 2008.

16. Day, C.M., D.M. Bullock, and J.R. Sturdevant, “Cycle Length Performance Measures: Revisiting and Extending Fundamentals,” Transportation Research Record, Paper ID: 09-0061, submitted July 2008, revised November 2008, under review.



31

Figure 1: Example Virginia DOT Dashboard (http://dashboard.virginiadot.org/)



32

Figure 2: First Level Performance Measure Drill Down.



33

Figure 3: Traffic Signal Report Card (http://www.ite.org/REPORTCARD/ )



34

Figure 4: Downloading files from remote signal controller via FTP over a virtual private network (VPN).



35

Figure 5: High-level flowchart for extracting performance measures from signal event data.

Import Data from Raw Data Log File

Process phase state changes, identify cycle boundaries, measure

cycle length, and assign cycle ID #

For each phase, count vehicles for each phase

instance

Associate phase data with cycles to calculate

phase level performance measures

Aggregate across phases to calculate intersection level

performance measures

1

2 3

4

5

Aggregate across intersections to develop

system-level performance measures

6



36

(a) Ring diagram showing the eight-phase dual-ring structure.

(b) Blocks and rings in the eight-phase dual-ring structure.

Figure 6: Divisions of time in a standard eight-phase dual-ring controller.

Protected

Permitted

Overlap

Movements

2

6

1

5

4

8

3

7

Ring 1, Block 1

Phases 1, 2

Ring 1, Block 2

Phases 3, 4

Ring 2, Block 1

Phases 5, 6

Ring 2, Block 2

Phases 7, 8

Block 1 Block 2

Ring 1

Ring 2

Barrier 1 Barrier 1Barrier 2



37

(a) Measuring cycle length from the time between similar barrier crossings.

(b) Measuring cycle length during free or low volume coordinated operation, when phase omits strongly influence observable points.

Figure 7: Explanation of cycle length measurement.

3 4 1 2

7 8 5 6

41 2

7 86

Ba

rrie

r 1

Ba

rrie

r 2

Ba

rrie

r 1

Ba

rrie

r 2

Ba

rrie

r 1

Block 1 Block 1Block 2 Block 2

Cycle Length

2 3 4

5 6 7 8

2 3 4

5 6 8

Barr

ier

1

Barr

ier

2

Barr

ier

2

Barr

ier

1

Block 2 Block 2Block 1Block 1

Cycle Length

5 6

1

6

Barr

ier

1



38

Figure 8: Cycle length, SR 32 and SR 37, November 12, 2008.

0

50

100

150

200

250

300

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Cy

cle

Len

gth

20-point Moving

Average



39

Table 1: Details of measuring cycle length. (a) Table of cycle events. Each line represents a time when the signal phase states are

changed by the controller.

Intersection ID Date

Event Time

Phase State

Block Cycle Boundary Event Flag

Cycle Number 1 2 3 4 5 6 7 8

1001 11/12/2008 13:22:48.1 0 1 0 0 1 0 0 0 1 554 1001 11/12/2008 13:23:09.5 0 0 1 0 0 0 1 0 2 1 555

1001 11/12/2008 13:23:27.2 0 0 1 0 0 0 0 1 2 555

1001 11/12/2008 13:23:34.5 0 0 0 1 0 0 0 1 2 555

1001 11/12/2008 13:24:11.5 1 0 0 0 0 1 0 0 1 555 1001 11/12/2008 13:24:27.4 0 1 0 0 0 1 0 0 1 555

1001 11/12/2008 13:24:40.5 0 1 0 0 1 0 0 0 1 555

1001 11/12/2008 13:25:03.9 0 0 1 0 0 0 1 0 2 1 556

1001 11/12/2008 13:25:17.4 0 0 1 0 0 0 0 1 2 556

1001 11/12/2008 13:25:18.5 0 0 0 1 0 0 0 1 2 556 1001 11/12/2008 13:26:00.1 0 1 0 0 0 1 0 0 1 556

1001 11/12/2008 13:26:26.0 0 1 0 0 1 0 0 0 1 556

1001 11/12/2008 13:26:47.9 0 0 1 0 0 0 1 0 2 1 557

1001 11/12/2008 13:27:01.4 0 0 1 0 0 0 0 1 2 557

(b) Example cycle length data table.


Beginning of Cycle

End of Cycle

Cycle Length

Cycle Number

1001 11/12/2008 13:21:35.5 13:23:09.5 94.0 554

1001 11/12/2008 13:23:09.5 13:25:03.9 114.4 555

1001 11/12/2008 13:25:03.9 13:26:47.9 104.0 556 1001 11/12/2008 13:26:47.9 13:28:31.9 104.0 557

1001 11/12/2008 13:28:31.9 13:30:15.9 104.0 558

1001 11/12/2008 13:30:15.9 13:31:58.8 102.9 559



40

(a) Measuring the length of the green indication from observable phase events.

(b) Relationship of effective green to the observable green indication.

Figure 9: Measuring green time.

1

0

tG

Time

G

Phase OffPhase On

tY

tR

tOFF

Phase

On/Off

Y R

Split

Beginning

of Green

End of

Green

End of

Yellow

End of

Phase

Red (Phase Off) Green

Ye

llow

&

Re

d C

lea

r

Flo

w R

ate

Phase

Sta

te

No movement

Saturation Flow

Red

(Phase Off)

I1

e I2

Effective Green

Cycle Length



41

Figure 10: Green time, phase 4, SR 32 and SR 37, November 12, 2008.

Table 2: Example data table for green time. Intersection ID Date

Cycle Time Phase

Cycle No.

Beginning of Green Phase Off

Split Time

Clearance Interval Green Time Yellow All Red

1001 11/12/2008 13:21:35.5 4 554 13:21:50.5 13:22:14.7 24.2 3.9 2.0 18.3

1001 11/12/2008 13:23:09.5 4 555 13:23:34.5 13:24:11.6 37.1 3.9 2.0 31.2

1001 11/12/2008 13:25:03.9 4 556 13:25:18.5 13:26:00.1 41.6 3.9 2.0 35.7

1001 11/12/2008 13:26:47.9 4 557 13:27:02.5 13:27:43.6 41.1 3.9 2.0 35.2 1001 11/12/2008 13:28:31.9 4 558 13:28:46.5 13:29:25.4 38.9 3.9 2.0 33.0

1001 11/12/2008 13:30:15.9 4 559 13:30:30.5 13:30:58.2 27.7 3.9 2.0 21.8

0

10

20

30

40

50

60

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Gre

en

Tim

e

20-point Moving

Average



42

Figure 11: Green time, eight phases, SR 32 and SR 37, November 12, 2008. The black lines show a 20-point moving averages.

Time of Day

Gre

en

Tim

e (s

ec

)

90

0

45

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

90

0

45

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W



43

Figure 12: Percentage of phases with pedestrian calls, Northwestern and Stadium, West Lafayette, Indiana.

P2 P4

P8P6

0:00 12:00 24:00 0:00 12:00 24:00

0%

100%

50%

0%

100%

50%

Week Before Fall Semester (8/15/07)

1st Week of Fall Semester (8/22/07)



44

Figure 13: Comparison of presence and count detection.

(a) Reno A&E

(b) EDI

(c) GTT

Figure 14: Example loop detector cards capable of producing count output.

1 0

t = t2

t = t0

t = t1

t = t3

1 0

Presence Count

incre

asin

g t

ime

t = t4

1

1

1

1

2

2

2

2

1

Stop bar detector



45

Figure 15: Counting intervals for vehicles.

Ring Diagram2

6

1

5

3

7

4

8

2

6

1

5

3

7

4

8

1

0

Phase 4 Green

1

5

2

6

OffOn

3

7

4

8

OffOn OffOn

Phase 4Cycle n

Phase 4Counts

2Block 1 2 1 2 1

Cycle Cycle n – 1 Cycle n Cycle n+1

Phase 4Cycle n + 1Counting Intervals

Adjustment forVehicle Utilization

of Clearance Time



46

Figure 16: Permitted left turn logic.

1

0

Phase 7 State

1

0

Block 2 State

Phase 7

Arrivals A B C

On

On Off On Off

Off On

1

0PLT Logic False True False (Not PLT) True

Ring Diagram2

6

1

5

3

7

4

8

3

7

4

8

Block2 21

1

0

Phase 7 Indication GreenArrow

Red Ball GreenArrow

Dark Dark

1

0

Phase 4 State On Off OnOff

R

Y

G

R

Y

G

R

Y

G

R

Y

G

R

Y

G



47

Figure 17: Vehicle counts, phase 4, SR 32 and SR 37, November 12, 2008.

Table 3: Example vehicle count data table. Intersection ID Date Cycle Time Phase Cycle No.

Cycle Length

Last End of Green

End of Green

e, Adjustment Factor

Vehicle Count

1001 11/12/2008 13:21:35.5 4 554 94.0 13:20:28.2 13:22:08.8 2.0 9 1001 11/12/2008 13:23:09.5 4 555 114.4 13:22:08.8 13:24:05.7 2.0 14

1001 11/12/2008 13:25:03.9 4 556 104.0 13:24:05.7 13:25:54.2 2.0 21

1001 11/12/2008 13:26:47.9 4 557 104.0 13:25:54.2 13:27:37.7 2.0 6

1001 11/12/2008 13:28:31.9 4 558 104.0 13:27:37.7 13:29:19.5 2.0 7

1001 11/12/2008 13:30:15.9 4 559 102.9 13:29:19.5 13:30:52.3 2.0 4

0

5

10

15

20

25

30

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Co

un

t

20-point Moving

Average



48

Figure 18: Vehicle counts, eight phases, SR 32 and SR 37, November 12, 2008. The black lines show a 20-point moving averages.

Time of Day

Co

un

ts

60

0

30

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

60

0

30

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W



49

Figure 19: Equivalent hourly flow rate, phase 4, SR 32 and SR 37, November 12, 2008.

Table 4: Example equivalent hourly flow rate data table.

Intersection ID Date Cycle Time Phase Cycle No.

Cycle Length (s)

Vehicle Count

Equivalent Hourly Flow Rate (veh/h)

1001 11/12/2008 13:21:35.5 4 554 94.0 9 345 1001 11/12/2008 13:23:09.5 4 555 114.4 14 441

1001 11/12/2008 13:25:03.9 4 556 104.0 21 727

1001 11/12/2008 13:26:47.9 4 557 104.0 6 208

1001 11/12/2008 13:28:31.9 4 558 104.0 7 242

1001 11/12/2008 13:30:15.9 4 559 102.9 4 140

0

100

200

300

400

500

600

700

800

900

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Eq

uiv

ale

nt

Ho

url

y F

low

Rate

(veh

/h)

20-point Moving

Average



50

Figure 20: Equivalent hourly flow rate, eight phases, SR 32 and SR 37, November 12, 2008. The black lines show 20-point moving averages.

Time of Day

Vo

lum

e (v

eh

/h)

1500

0

750

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

1500

0

750

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W



51

Figure 21: V/C Ratio, phase 4, SR 32 and SR 37, November 12, 2008.

Table 5: V/C Ratio example data table.


Cycle Time Phase

Cycle No.

Green Time

Saturation Flow Rate Count

Volume-to-Capacity Ratio

1001 11/12/2008 13:21:35.5 4 554 18.3 1900 9 0.932

1001 11/12/2008 13:23:09.5 4 555 31.2 1900 14 0.850

1001 11/12/2008 13:25:03.9 4 556 35.7 1900 21 1.115

1001 11/12/2008 13:26:47.9 4 557 35.2 1900 6 0.323 1001 11/12/2008 13:28:31.9 4 558 33.0 1900 7 0.402

1001 11/12/2008 13:30:15.9 4 559 21.8 1900 4 0.348

0

0.2

0.4

0.6

0.8

1

1.2

1.4

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

V/C

Rati

o

20-point Moving

Average



52

Figure 22: V/C Ratio, eight phases, SR 32 and SR 37, November 12, 2008. The black lines show 20-point moving averages.

Figure 23: Number of split failures per half hour bin, eight phases, SR 32 and SR 37, November 12, 2008.

Time of Day

oita

Ryti

ca

pa

C-ot-

em

ulo

V

1

0

0.5

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

1

0

0.5

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W

1.5

1.5

Time of Day

Nu

mb

er o

f Sp

lit

Fa

ilu

res

pe

r 3

0 m

in

14

0

7

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

14

0

7

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W



53

Figure 24: Distributions of reasons for phase termination by time of day, eight phases, SR 32 and SR 37, November 12, 2008..

100%

0

50%

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

100%

0

50%

0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00 0:00 24:0012:00

Time of Day

Pe

rce

nta

ge o

f Ph

as

es

pe

r 3

0 m

in

P1SL

P2N

P3WL

P4E

P6S

P5NL

P7EL

P8W

Force-off

Gap out

Omit



54

Figure 25: Calculating percent arriving on green.

Ring Diagram4

8

3

7

1

5

2

6

4

8

3

7

1

5

2

6

1

0

Phase 2 State

3

7

4

8

OffOn

1

5

2

6

OffOnOff On

Phase 2Counts

Cycle Cycle n Cycle n+1 Cycle n+2

1

0

Phase 2 Indication RedGreen RedGreenRed Green

Y + AR – ε

G



55

Figure 26: Proportion of vehicles arriving on green, phase 2, SR 37 & SR 32, November 11, 2008.

Table 6: Example data table for proportion of vehicles arriving on green.

Int. ID Date

Cycle Time Phase

Cycle No.

Last End of Green (LEOG)

Beginning of Green (BOG)

End of Green (EOG)

ε, EOG Adjustment Factor

Arrivals on Green

Arrivals on Red POG

1001 11/12/2008 13:21:35.5 2 554 13:21:29.5 13:22:14.7 13:23:03.5 0.0 10 8 0.556

1001 11/12/2008 13:23:09.5 2 555 13:23:03.5 13:24:27.5 13:24:57.9 0.0 9 8 0.529

1001 11/12/2008 13:25:03.9 2 556 13:24:57.9 13:26:00.1 13:26:41.9 0.0 9 4 0.692

1001 11/12/2008 13:26:47.9 2 557 13:26:41.9 13:27:55.4 13:28:25.9 0.0 11 5 0.688 1001 11/12/2008 13:28:31.9 2 558 13:28:25.9 13:29:25.4 13:30:09.9 0.0 7 8 0.467

1001 11/12/2008 13:30:15.9 2 559 13:30:09.9 13:30:58.2 13:31:52.8 0.0 9 8 0.529

0

0.2

0.4

0.6

0.8

1

1.2

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Perc

en

t A

rriv

ing

on

Gre

en

20-point Moving

Average



56

Figure 27: Definition of the epsilon term in adjusting for vehicle arrivals on red and green at an advance detector.

Figure 28: Sensitivity of Percentage on Green (20 point moving average lines shown) to epsilon term used to adjust the end of green cutoff point.

Red Green Yellow AR Red

0 642–2–4–6

Arrivals on Green Arrivals on Red

for next cycle

ε

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00

Time of Day

Pe

rcen

tag

e o

n G

reen

+6

+4

+2

+0

–2

–4

–6



57

Figure 29: Purdue Progression Diagram by cycle time by time of day for one cycle.

0

20

40

60

80

100

120

140

160

180

20013:2

5:0

6

13:2

5:1

2

13:2

5:1

8

13:2

5:2

4

13:2

5:3

0

13:2

5:3

6

13:2

5:4

2

13:2

5:4

8

13:2

5:5

4

13:2

6:0

0

13:2

6:0

6

13:2

6:1

2

13:2

6:1

8

13:2

6:2

4

13:2

6:3

0

13:2

6:3

6

13:2

6:4

2

Time of Day

Tim

e i

n C

ycle

End of Phase / End of Cycle

Beginning of Green

Beginning of Cycle

End of Green



58

Figure 30: Purdue Progression Diagram for northbound phase 2 at SR 32 & SR 37 in Noblesville, Indiana for 24 hours.

0

20

40

60

80

100

120

140

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Tim

e in

Cycle

A

B

C

D



59

Figure 31: Purdue Progression Diagram for northbound phase 6 at SR 37 and Pleasant St. over 24 hours for November 12, 2008.

0

20

40

60

80

100

120

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Tim

e i

n C

yc

le

0

0.25

0.5

0.75

1

PO

G

20-point Moving

Average

AB



60

Table 7: Arrival type definition table, based on HCM Exhibit 15-4.

Arrival Type

Range of Platoon Ratio

Default Value of Rp

Progression Quality

Interpolated Arrival Type Equation

1 Rp ≤ 0.50 0.333 Very poor 12 +pR

2 0.50 < Rp ≤ 0.85 0.667 Unfavorable

−+

35.0

85.03

35.0

pR

3 0.85 < Rp ≤ 1.15 1.000 Random arrivals

−+

3.0

15.14

3.0

pR

4 1.15 < Rp ≤ 1.50 1.333 Favorable

−+

35.0

5.15

35.0

pR

5 1.50 < Rp ≤ 2.00 1.667 Highly

favorable 22 +pR

6 Rp > 2.00 2.000 Exceptional 6

Figure 32: Interpolated and integer arrival type plotted against Platoon Ratio.

0

1

2

3

4

5

6

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25

Platoon Ratio

Arr

ival

Typ

e

Integer AT

Interpolated AT

0.5

0.85

1.15

1.5

2



61

Figure 33: Arrival type, phase 2, SR 32 and SR 37, November 12, 2008.

Table 8: Example arrival type data table.

Int.ID Date Cycle Time Phase

Cycle No. POG

Green time

Cycle length

g/C Ratio Rp AT AT (interpolated)

1001 11/12/2008 13:21:35.5 2 554 0.556 48.8 94.0 0.519 1.07 3 3.73 1001 11/12/2008 13:23:09.5 2 555 0.529 30.4 114.4 0.266 1.99 5 5.98

1001 11/12/2008 13:25:03.9 2 556 0.692 41.8 104.0 0.402 1.72 5 5.44

1001 11/12/2008 13:26:47.9 2 557 0.688 30.5 104.0 0.293 2.34 6 6.00

1001 11/12/2008 13:28:31.9 2 558 0.467 44.5 104.0 0.428 1.09 3 3.80

1001 11/12/2008 13:30:15.9 2 559 0.529 54.6 102.9 0.531 1.00 3 3.49

0

1

2

3

4

5

6

7

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00

Time of Day

Arr

ival

Typ

e

20-point Moving

Average



62

(a) Arrival Profile.

(b) Departure Profile.

(c) Combined Arrival and Departure Profile.

Figure 34: An example of a input-output method queue polygon.

Time (s)

Nu

mb

er

of

Veh

icle

s

Arrival Profile

Departure Profile

Time (s)

Nu

mb

er

of

Veh

icle

s

BOG+δ

Time (s)

Nu

mb

er

of

Veh

icle

s

BOG+δ EOGLEOGti

t(i –1)

Approximation of discrete vehicle departures as a continuous function



63

(a) Rectangular.

(b) Triangular.

(c) Trapezoidal.

Figure 35: The three main types of intervals for calculating delay using the input-output queue polygon method.

Time (s)

Nu

mb

er

of

Ve

hic

les

vi–1

vi

ti–1

ti

Time (s)

Nu

mb

er

of

Ve

hic

les

vi–1

ti–1

ti

tD

time to

discharge

Time (s)

Nu

mb

er

of

Ve

hic

les v

i–1

ti–1

ti

tD

time todischarge

vr



64

Figure 36: Input-Output Delay, phase 2, SR 32 and SR 37, November 12, 2008.

0

5

10

15

20

25

30

35

40

45

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Inp

ut-

Ou

tpu

t D

ela

y (

se

c/v

eh

)

20-point Moving

Average

Ta

ble

9:

Exa

mp

le c

alc

ula

tio

n o

f in

pu

t/o

utp

ut d

ela

y f

or

a b

usy in

sta

nce

of

pha

se

2 o

n N

ove

mb

er

12

, 2

00

8.

i E

vent

T

ype

Que

ue

Dis

char

ge

Eve

nt T

ime

t i –

t i–1

Inte

rval

D

urat

ion

c i (v

eh)

Inte

rval

C

apac

ity

v i–1

V

ehic

les

in S

yste

m

t D –

t i–1

T

ime

to

Dis

char

ge

v i–1

– v

r D

isch

arge

d V

ehic

les

v r

Res

idua

l V

ehic

les

Cle

ar

Fla

g In

terv

al

Del

ay

Tot

al

Del

ay

Veh

icle

C

ount

A

vera

ge

Del

ay

0 LE

OG

1

17

:30:

45.0

-

- -

- -

2.0

- -

- 2

1 V

ehic

le

17

:30:

45.9

0.

9 0.

0 2.

0 2.

1 0.

0 2.

0

1.8

1.8

3

2 V

ehic

le

17

:30:

47.1

1.

2 0.

0 3.

0 3.

2 0.

0 3.

0

3.6

5.4

4

3 V

ehic

le

17

:30:

48.5

1.

4 0.

0 4.

0 4.

2 0.

0 4.

0

5.6

11.0

5

4

Veh

icle

17

:30:

48.6

0.

1 0.

0 5.

0 5.

3 0.

0 5.

0

0.5

11.5

6

5 V

ehic

le

17

:30:

50.9

2.

3 0.

0 6.

0 6.

3 0.

0 6.

0

13.8

25

.3

7

6 V

ehic

le

17

:30:

52.6

1.

7 0.

0 7.

0 7.

4 0.

0 7.

0

11.9

37

.2

8

7 V

ehic

le

17

:30:

53.1

0.

5 0.

0 8.

0 8.

4 0.

0 8.

0

4.0

41.2

9

8

Veh

icle

17

:30:

54.7

1.

6 0.

0 9.

0 9.

5 0.

0 9.

0

14.4

55

.6

10

9 V

ehic

le

17

:31:

07.3

12

.6

0.0

10.0

10

.6

0.0

10.0

126.

0 18

1.6

11

10

Veh

icle

17

:31:

08.9

1.

6 0.

0 11

.0

11.6

0.

0 11

.0

17

.6

199.

2 12

11

Veh

icle

17

:31:

14.2

5.

3 0.

0 12

.0

12.7

0.

0 12

.0

63

.6

262.

8 13

12

Veh

icle

17

:31:

14.6

0.

4 0.

0 13

.0

13.7

0.

0 13

.0

5.

2 26

8.0

14

13

V

ehic

le

17

:31:

18.6

4.

0 0.

0 14

.0

14.8

0.

0 14

.0

56

.0

324.

0 15

14

Veh

icle

17

:31:

32.4

13

.8

0.0

15.0

15

.8

0.0

15.0

207.

0 53

1.0

16

15

BO

G2

17

:31:

56.8

24

.4

0.0

16.0

16

.9

0.0

16.0

390.

4 92

1.4

16

16

Veh

icle

�

17:3

2:03

.2

6.4

6.8

16.0

16

.9

6.8

9.2

80

.8

1002

.2

17

17

Veh

icle

�

17:3

2:06

.5

3.3

3.5

10.2

10

.8

3.5

6.8

28

.1

1030

.2

18

18

V

ehic

le

�

17:3

2:08

.7

2.2

2.3

7.8

8.2

2.3

5.4

14

.5

1044

.8

19

19

Veh

icle

�

17:3

2:14

.8

6.1

6.4

6.4

6.8

6.4

0.0

�

21.9

10

66.6

20

20

Veh

icle

�

17:3

2:16

.9

2.1

2.2

1.0

1.1

1.0

0.0

�

0.0

1066

.6

21

21

Veh

icle

�

17:3

2:18

.9

2.0

2.1

1.0

1.1

1.0

0.0

�

0.0

1066

.6

22

22

Veh

icle

�

17:3

2:21

.4

2.5

2.6

1.0

1.1

1.0

0.0

�

0.0

1066

.6

23

23

V

ehic

le

�

17:3

2:23

.9

2.5

2.6

1.0

1.1

1.0

0.0

�

0.0

1066

.6

24

24

Veh

icle

�

17:3

2:25

.8

1.9

2.0

1.0

1.1

1.0

0.0

�

0.0

1066

.6

25

25

Veh

icle

�

17:3

2:27

.6

1.8

1.9

1.0

1.1

1.0

0.0

�

0.0

1066

.6

26

26

Veh

icle

�

17:3

2:27

.6

0.0

0.0

1.0

1.1

0.0

1.0

�

0.0

1066

.6

27

27

E

OG

3

�

17:3

2:33

.4

5.8

6.1

2.0

2.1

2.0

0.0

�

0.0

1066

.6

27

39.5

1 L

ast E

nd o

f Gre

en.

2 B

egin

ning

of G

reen

(pl

us s

tart

-up

lost

tim

e).

3 E

nd o

f Gre

en.


Table 10: Definition of Level of Service (LOS) for HCM delay (HCM Exhibit 16

Figure 37: The influence of TX (volume/capacity ratio).

0

5

10

15

20

25

30

35

40

45

50

0 5

d2, In

cre

men

tal D

ela

y (

s)

Purdue University

66

Definition of Level of Service (LOS) for HCM delay (HCM Exhibit 16

T on the calculated incremental delay at various values of

(volume/capacity ratio). For this plot, I = 1 and k = 0.08.

10 15 20

Analysis Period, T (min)

X = 0.85

X = 0.75


Definition of Level of Service (LOS) for HCM delay (HCM Exhibit 16-2).

on the calculated incremental delay at various values of

25



67

Table 11: Values of k and kmin (HCM exhibit 16-13).



68

Figure 38: HCM estimated delay using 15-minute bins, phase 2, SR 32 and SR 37, November 12, 2008.

Table 12: Example data table for 15-minute HCM estimated delay.

Int.ID Date Bin Time Phase

Cycle Length

Green Time

Arrivals on Green

Total Arrivals

g/C Ratio

X2, V/C Ratio POG fPA PF

1001 11/12/2008 13:00:00 2 104.2 38.3 80 140 0.367 0.401 0.571 1.0 0.677

1001 11/12/2008 13:15:00 2 104.0 37.5 77 133 0.361 0.388 0.579 1.0 0.659 1001 11/12/2008 13:30:00 2 104.0 39.2 74 144 0.377 0.402 0.514 1.0 0.780

1001 11/12/2008 13:45:00 2 104.0 39.3 71 119 0.378 0.332 0.597 1.0 0.648

1001 11/12/2008 14:00:00 2 103.9 39.8 110 189 0.383 0.519 0.582 1.0 0.678

1001 11/12/2008 14:15:00 2 104.1 42.1 93 166 0.404 0.432 0.560 1.0 0.738

T Veh Ext kmin k I Capacity, c d1 d2 d1*PF HCM Delay 0.25 2.4 0.08 0.08 1 1395 24.5 0.1 16.6 16.7

0.25 2.4 0.08 0.08 1 1372 24.7 0.1 16.3 16.4

0.25 2.4 0.08 0.08 1 1433 23.8 0.1 18.6 18.7

0.25 2.4 0.08 0.08 1 1436 23.0 0.1 14.9 15.0

0.25 2.4 0.08 0.08 1 1457 24.7 0.2 16.7 16.9 0.25 2.4 0.08 0.08 1 1535 22.4 0.1 16.5 16.7

0

5

10

15

20

25

30

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

5-m

inu

te H

CM

De

lay

(se

c/v

eh

)LO

S A

LO

S B

LO

S C



69

Figure 39: HCM estimated delay using 5-minute bins, phase 2, SR 32 and SR 37, November 12, 2008.

Table 13: Example data table for 5-minute HCM estimated delay.

Int.ID Date Bin Time Phase

Cycle Length

Green Time

Arrivals on Green

Total Arrivals

g/C Ratio


1001 11/12/2008 13:15:00 2 103.9 32.8 27 43 0.316 0.430 0.628 1.0 0.544

1001 11/12/2008 13:20:00 2 104.2 40.9 26 49 0.392 0.395 0.531 1.0 0.772 1001 11/12/2008 13:25:00 2 104.0 38.9 24 41 0.374 0.346 0.585 1.0 0.663

1001 11/12/2008 13:30:00 2 104.0 37.5 24 51 0.361 0.447 0.471 1.0 0.828

1001 11/12/2008 13:35:00 2 104.0 37.3 25 43 0.358 0.379 0.581 1.0 0.652

1001 11/12/2008 13:40:00 2 104.0 42.9 25 50 0.413 0.383 0.500 1.0 0.851


0.25 2.4 0.08 0.08 1 1490 22.8 0.1 17.6 17.7

0.25 2.4 0.08 0.08 1 1423 23.4 0.1 15.5 15.6

0.25 2.4 0.08 0.08 1 1371 25.3 0.2 21.0 21.1

0.25 2.4 0.08 0.08 1 1362 24.8 0.1 16.2 16.3 0.25 2.4 0.08 0.08 1 1568 21.3 0.1 18.1 18.3

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

5-m

inu

te H

CM

De

lay

(se

c/v

eh

)

12-point Moving Average

LO

S A

LO

S B

LO

S C

LO

S D



70

Figure 40: Cycle-by-cycle HCM estimated delay, phase 2, SR 32 and SR 37, November 12, 2008.

Table 14: Example data table for cycle-by-cycle HCM estimated delay.

Int.ID Date Cycle Time Phase Cycle No.

Cycle Length

Green Time

g/C Ratio


1001 11/12/2008 13:21:35.5 2 554 94.0 48.8 0.519 0.388 0.556 1.0 0.924

1001 11/12/2008 13:23:09.5 2 555 114.4 30.4 0.266 0.499 0.529 1.0 0.641 1001 11/12/2008 13:25:03.9 2 556 104.0 41.8 0.402 0.317 0.692 1.0 0.514

1001 11/12/2008 13:26:47.9 2 557 104.0 30.5 0.293 0.497 0.688 1.0 0.442

1001 11/12/2008 13:28:31.9 2 558 104.0 44.5 0.428 0.341 0.467 1.0 0.932

1001 11/12/2008 13:30:15.9 2 559 102.9 54.6 0.531 0.278 0.529 1.0 1.003


0.032 2.4 0.08 0.08 1 1010 35.5 0.3 22.8 23.1

0.029 2.4 0.08 0.08 1 1527 21.3 0.1 11.0 11.1

0.029 2.4 0.08 0.08 1 1114 30.4 0.3 13.4 13.7

0.029 2.4 0.08 0.08 1 1626 19.9 0.1 18.6 18.7 0.029 2.4 0.08 0.08 1 2016 13.3 0.1 13.3 13.4

0

5

10

15

20

25

30

35

40

45

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Cy

cle

-by

-Cy

cle

HC

M E

sti

ma

ted

De

lay

(s

ec

/ve

h)

20-point Moving

Average

LO

S A

LO

S B

LO

S C

LO

S D



71

(a) Superimposed 24-hour plots.

(b) Cumulative total delay.

Figure 41: Comparison of 15-minute delay, 5-minute, and cycle-by-cycle delay.

0

5

10

15

20

25

30

35

40

45

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Dela

y (

s/v

eh

)

C-by-C 15-min 5-min 20 per. Mov. Avg. (C-by-C) 12 per. Mov. Avg. (5-min)

15-minute

Cycle-by-Cycle

5-minute

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Cu

mu

lati

ve T

ota

l D

ela

y (

s)

C-by-C 15min 5min

Cycle-by-Cycle

5-minute

15-minute



72

(a) Breakdown of cycle-by-cycle delay uniform and incremental terms.

(b) Amounts of cumulative total delay due to uniform and incremental terms.

Figure 42: How uniform and incremental delay contribute to the total HCM estimated

delay.

0

5

10

15

20

25

30

35

40

45

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Cy

cle

-by-C

ycle

HC

M E

sti

ma

ted

Dela

y (

se

c/v

eh

)

PF(d1) + d2

PF(d1)

d2

0

20000

40000

60000

80000

100000

120000

140000

160000

Cu

mu

lati

ve

To

tal d

1*P

F (

s)

C-by-C 15min 5min

0

2000

4000

6000

8000

10000

12000

14000

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Cu

mu

lati

ve T

ota

l d

2 (

s)

Cycle-by-Cycle

5-minute

15-minute

Cycle-by-Cycle

5-minute,

15-minute



73

(a) Superimposed plots of 20-point moving averages of cycle-by-cycle HCM and input-

output (IO) delay over 24 hours.

(b) Plot of cycle-by-cycle HCM delay versus input-output delay.

Figure 43: Comparison of cycle-by-cycle HCM delay to input-output delay.

0

5

10

15

20

25

30

35

40

45

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Dela

y (

se

c/v

eh

)

HCM Delay

IO Delay

y = 0.9164x + 0.8503

R2 = 0.7492

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45

HCM Delay (s/veh)

Inp

ut-

Ou

tpu

t D

ela

y (

s/v

eh

)



74

Table 15: Descriptive statistics comparing cycle-by-cycle HCM delay to input-output (IO) delay by TOD plan pattern.

Time Period Count Type Average St. Dev. Min Max

Free/Overnight 449 HCM 3.4 5.9 0.0 26.8 IO 3.0 6.4 0.0 43.0

AM Peak 92 HCM 7.0 7.7 0.0 27.9

IO 5.9 6.5 0.0 30.8

Off Peak 75 HCM 8.0 5.7 0.0 27.5 IO 10.2 7.9 0.0 34.9

Midday 70 HCM 10.7 5.5 0.1 25.7 IO 11.6 6.3 0.0 31.1

Off Peak 70 HCM 17.7 6.7 4.2 35.0 IO 19.3 8.6 5.2 41.4

PM Peak 124 HCM 23.2 7.9 5.4 42.4 IO 21.3 8.0 6.6 39.5

Evening 104 HCM 11.7 5.7 0.0 23.9 IO 14.5 8.3 0.0 34.9

24 hours 984 HCM 9.0 9.3 0.0 42.4 IO 9.1 9.9 0.0 43.0



75

Figure 44: Explanation of critical path.

1 2

5 6

3 4

7 8

3 41 2

(a) Critical Path 1234

1 2

5 6

3 4

7 8

1 2

7 8

(b) Critical Path 1278

1 2

5 6

3 4

7 8

3 4

5 6

(c) Critical Path 5634

1 2

5 6

3 4

7 875 6 8

(d) Critical Path 5678



76

Figure 45: Degree of intersection saturation (XC), SR 37 and 32, November 12, 2008.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Inte

rsecti

on

Satu

rati

on

1234

1278

5634

5678

20 pt. Mov. Avg.



77

Table 16: Example data tables for Block 1 XC calculations.

(a) Ring 1, Block 1 (R1B1: Phases 1 and 2)

Int.ID Date Cycle Time

Phase 1 Phase 2 Phase 1 & 2 Lost Time R1B1 V/S V1 S1 V1/S1 V2 S2 V2/S2 L1 L2 L(1+2)

1001 11/12/2008 13:21:35.5 0 1900 0.000 766 3800 0.202 0.0 6.0 6.0 0.202 1001 11/12/2008 13:23:09.5 94 1900 0.050 503 3800 0.132 5.0 6.0 11.0 0.182

1001 11/12/2008 13:25:03.9 0 1900 0.000 485 3800 0.128 0.0 6.0 6.0 0.128

1001 11/12/2008 13:26:47.9 35 1900 0.018 554 3800 0.146 5.0 6.0 11.0 0.164

1001 11/12/2008 13:28:31.9 0 1900 0.000 554 3800 0.146 0.0 6.0 6.0 0.146 1001 11/12/2008 13:30:15.9 0 1900 0.000 560 3800 0.147 0.0 6.0 6.0 0.147

(b) Ring 2, Block 1 (R2B1: Phases 5 and 6)



1001 11/12/2008 13:21:35.5 191 1900 0.101 574 3800 0.151 6.0 6.0 12.0 0.252

1001 11/12/2008 13:23:09.5 315 1900 0.166 346 3800 0.091 6.0 6.0 12.0 0.257

1001 11/12/2008 13:25:03.9 208 1900 0.109 588 3800 0.155 6.0 6.0 12.0 0.264 1001 11/12/2008 13:26:47.9 312 1900 0.164 588 3800 0.155 6.0 6.0 12.0 0.319

1001 11/12/2008 13:28:31.9 277 1900 0.146 346 3800 0.091 6.0 6.0 12.0 0.237

1001 11/12/2008 13:30:15.9 385 1900 0.203 630 3800 0.166 6.0 6.0 12.0 0.368

(c) Block 1 Critical Path Determination


Cycle No.

Compared Values Lost Times Chosen Values

R1B1 V/S R2B1 V/S L(1+2) L(5+6)

Crit. Path

Lost Time

Block 1 V/S

1001 11/12/2008 13:21:35.5 554 0.202 0.252 6.0 12.0 56 12.0 0.252

1001 11/12/2008 13:23:09.5 555 0.182 0.257 11.0 12.0 56 12.0 0.257

1001 11/12/2008 13:25:03.9 556 0.128 0.264 6.0 12.0 56 12.0 0.264 1001 11/12/2008 13:26:47.9 557 0.164 0.319 11.0 12.0 56 12.0 0.319

1001 11/12/2008 13:28:31.9 558 0.146 0.237 6.0 12.0 56 12.0 0.237

1001 11/12/2008 13:30:15.9 559 0.147 0.368 6.0 12.0 56 12.0 0.368



78

Table 17: Example data tables for Block 2 XC calculations.

(a) Ring 1, Block 2 (Phases 3 and 4)



1001 11/12/2008 13:21:35.5 115 1900 0.060 345 1900 0.181 5.2 5.9 11.1 0.242 1001 11/12/2008 13:23:09.5 157 1900 0.083 441 1900 0.232 5.2 5.9 11.1 0.315

1001 11/12/2008 13:25:03.9 173 1900 0.091 727 1900 0.383 5.2 5.9 11.1 0.474

1001 11/12/2008 13:26:47.9 138 1900 0.073 208 1900 0.109 5.2 5.9 11.1 0.182

1001 11/12/2008 13:28:31.9 173 1900 0.091 242 1900 0.128 5.2 5.9 11.1 0.219 1001 11/12/2008 13:30:15.9 245 1900 0.129 140 1900 0.074 5.2 5.9 11.1 0.203

(b) Ring 2, Block 2 (Phases 7 and 8)



1001 11/12/2008 13:21:35.5 77 1900 0.040 153 3800 0.040 5.2 5.9 11.1 0.081

1001 11/12/2008 13:23:09.5 31 1900 0.017 252 3800 0.066 5.2 5.9 11.1 0.083

1001 11/12/2008 13:25:03.9 104 1900 0.055 138 3800 0.036 5.2 5.9 11.1 0.091 1001 11/12/2008 13:26:47.9 173 1900 0.091 312 3800 0.082 5.2 5.9 11.1 0.173

1001 11/12/2008 13:28:31.9 138 1900 0.073 277 3800 0.073 5.2 5.9 11.1 0.146

1001 11/12/2008 13:30:15.9 0 1900 0.000 315 3800 0.083 0.0 5.9 5.9 0.083

(c) Block 2 Critical Path Determination


Cycle No.

Compared Values Lost Times Chosen Values

R1B2 V/S R2B2 V/S L(3+4) L(7+8)

Crit. Path

Lost Time

Block 2 V/S

1001 11/12/2008 13:21:35.5 554 0.242 0.081 11.1 11.1 34 11.1 0.242

1001 11/12/2008 13:23:09.5 555 0.315 0.083 11.1 11.1 34 11.1 0.315

1001 11/12/2008 13:25:03.9 556 0.474 0.091 11.1 11.1 34 11.1 0.474 1001 11/12/2008 13:26:47.9 557 0.182 0.173 11.1 11.1 34 11.1 0.182

1001 11/12/2008 13:28:31.9 558 0.219 0.146 11.1 11.1 34 11.1 0.219

1001 11/12/2008 13:30:15.9 559 0.203 0.083 11.1 5.9 34 11.1 0.203



79

Table 18: Example XC data table showing final calculation steps.


Cycle No.

Block 1 V/S

Block 2 V/S

Sum (V/S)

Block 1 LT

Block 2 LT

Total LT

Cycle Length

C/ (C-L) XC CP

1001 11/12/2008 13:21:35.5 554 0.252 0.242 0.494 12.0 11.1 23.1 94.0 1.326 0.655 5634

1001 11/12/2008 13:23:09.5 555 0.257 0.315 0.571 12.0 11.1 23.1 114.4 1.253 0.716 5634

1001 11/12/2008 13:25:03.9 556 0.264 0.474 0.738 12.0 11.1 23.1 104.0 1.286 0.949 5634

1001 11/12/2008 13:26:47.9 557 0.319 0.182 0.501 12.0 11.1 23.1 104.0 1.286 0.644 5634 1001 11/12/2008 13:28:31.9 558 0.237 0.219 0.455 12.0 11.1 23.1 104.0 1.286 0.586 5634

1001 11/12/2008 13:30:15.9 559 0.368 0.203 0.571 12.0 11.1 23.1 102.9 1.289 0.736 5634

Figure 46: XC graph with split failures, SR 37 and SR 32, November 12, 2008.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time of Day

Inte

rse

cti

on

Sa

tura

tio

n

Phase 1 Phase 2

Phase 3 Phase 4

Phase 5 Phase 6

Phase 7 Phase 8

Example of

Multiple failures in

cycle (P3, P5)

20-point Moving

Average for all cycles

(with and without

split failures)

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