MINIMIZATION OF OVERALL PERSON DELAY AT LIGHT RAIL TRANSIT

CROSSINGS ON CONGESTED URBAN ARTERIALS

by

Nikola Mitrovic

A Thesis Submitted to the Faculty of

College of Engineering and Computer Science

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

Florida Atlantic University

Boca Raton, Florida

May 2011

ii

Copyright by Nikola Mitrovic 2011

MINIMIZATIO OF OVERALL PERSO DELAY AT LIGHT RAIL TRANSIT

CROSSINGS 0 CO GESTED URBAN ARTERIALS

By

ikola Mitrovic

This thesis was prepared under the direction of the candidate' thesis advisor, Dr.Aleksandar Stevanovic, Department of Civi~ Environmenta~ and GeomaticsEngineering, and has been approved by the members ofhis supervisory committee. It wassubmitted to the faculty of the College of Engineering and Computer Science and wasaccepted in partial fulfillment of the requirements for the degree ofMaster of Science.

SUPERVISORY COMMITTEE:

IteetSewda/ 51eJ(;UA6V/CAleksandar tevanovic, Ph.D.Thesis or

~JiL~P.D. Scarlatos, Ph.D. :=Chair, Department of Civil, Environmentaland Geomatics Engineering

Karl . Steven ,Dean, College f ngineering and Computer Science

!7R:I~~Dean, Graduate College

111

~~Khaled Sobhan, Ph.D.

fJ!,.;)/5; U'I;Date r (

iv

ACKNOWLEDGEMENT

This research is the result of two years of hard work and a lot of determination.

Nonetheless, none of this would have been possible without the help, support and

encouragement of the faculty and student body of the Transportation Research Group at

Florida Atlantic University.

I would like to convey my gratitude to my advisor, Dr. Aleksandar Stevanovic. His

supervision, guidance and advice throughout the different stages of this paper were key to

the completion of my research. Dr. Stevanovic has inspired and enriched my growth as a

student, a researcher and a scientist.

A special thanks go to the Utah Transit Authority (UTA) and Utah Department of

Transportation (UDOT) for providing critical data used for this study, especially to Mrs.

Kerry Doene, Strategic Planner (UTA).

In addition, I would like to thank Dr. Evangelos Kaisar and Mrs Jarice Rodriguez for

their help and preparation of the thesis. And last but not least my transportation

colleagues, Ioannis Psarros, Dusan Jolovic, Claudia Olarte and Benazir Portal. Thank you

for your continuous support, motivation and encouragement

v

ABSTRACT

Author: Nikola Mitrovic

Title: Minimization of Overall Person Delay at Light Rail Transit

Crossings on Congested Urban Arterials

Institution: Florida Atlantic University

Thesis Advisor: Dr. Aleksandar Stevanovic

Degree: Master of Science

Year: 2011

This study describes analytical model as one innovative way to simulate Light Rail

Transit (LRT) operations and calculate vehicular, transit and person delays at LRT

crossings through Microsoft Excel. Analytical model emulates LRT trajectories from

field and use these trajectories to clearly define train and car phases through Visual Basic

for Applications (VBA) logic, which is part of analytical model. Simulation of train

trajectories and calculations of delays were done for different LRT strategies and

estimated roadway condition, Testing and validation of analytical model were performed

in one case study in Salt Lake City (UT). Results show that analytical model is capable of

emulating LRT trajectories and estimating delay at isolated LRT crossing. However,

analytical model is not capable of simulating different train strategies at two or more LRT

crossings, at the same time. Finally, extracted strategy provides savings from $100.000 to

$200.000 in study area, on annual basis for projected year.

vi

MINIMIZE PERSON DELAY AT RAILROAD CROSSING THROUGH SEARCH

BASED OPTIMIZATION TOOL

LIST OF TABLES ........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

1 INTRODUCTION ...................................................................................................... 1

1.1 Problem Statement ...............................................................................................2

1.2 Research Goals and Objectives ............................................................................3

1.3 Thesis Organization .............................................................................................3

2 LITERATURE REVIEW ........................................................................................... 5

2.1 Light Rail Operations ...........................................................................................5

2.2 Computation of Roadway Delay at Railroad Crossing ........................................8

3 NETWORK SIMULATION MODEL ..................................................................... 11

3.1 Case Study Area .................................................................................................11

3.2 Modeling process ...............................................................................................12

3.3 Calibration and Validation of VISSIM Model ...................................................15

3.3.1 Vehicular Data ............................................................................................ 15

3.3.2 Transit Data ................................................................................................. 17

3.4 Future Operations ...............................................................................................20

4 ANALYTICAL MODEL.......................................................................................... 21

4.1 Simulation of Train Trajectories ........................................................................21

vii

4.2 Calculation Vehicular, Transit and Person Delay ..............................................25

4.2.1 Vehicular Delay .......................................................................................... 26

4.2.2 Light Rail Transit Delay ............................................................................. 27

4.2.3 Person Delay ............................................................................................... 28

4.3 Validation of Analytical Model .........................................................................29

4.4 Simulation of Different Train Strategies ............................................................33

4.5 Limitations of Analytical Model ........................................................................35

5 RESULTS AND ANALYSIS ................................................................................... 37

5.1 Impact of Different Train Schedules on Overall Person Delay .........................38

5.2 Impact of Different LRT Priority Strategies ......................................................40

5.2.1 Different LRT Priorities at Crossing on 1300S SB .................................... 41

5.2.2 Different LRT Priorities at Crossing on 2100S NB .................................... 47

5.3 Person Delay Savings .........................................................................................52

6 DISCUSSION ........................................................................................................... 55

7 CONCLUSIONS AND FUTURE RECOMMENDATIONS ................................... 57

8 REFERENCES ......................................................................................................... 61

viii

LIST OF TABLES

Table 1: Recorded Parameters in VISSIM Simulation ..................................................... 26

Table 2: Overall Person Delay for Different Train Strategies .......................................... 38

Table 3: Overall Person Delay for Different LRT Strategies on 1300S ........................... 42

Table 4: Person Delay at Crossing on 1300S for Different Strategies on Same Crossing 43

Table 5: Significance of Results for Different Priority Strategies on 1300S .................... 45

Table 6: Overall Person Delay for Different LRT Strategies on 2100S ........................... 48

Table 7: Person Delay at Crossing on 2100S for Different Strategies on Same Crossing 49

Table 8: Significance of Results for Different Priority Strategies on 1300S .................... 50

Table 9: Person Demand at LRT Crossings ...................................................................... 53

Table 10: Saving Time at LRT Crossing .......................................................................... 53

Table 11: PM and Annual Overall Benefits ...................................................................... 54

ix

LIST OF FIGURES

Figure 1: Case Study Area ................................................................................................ 12

Figure 2: VISSIM Model of Study Area........................................................................... 13

Figure 3: Calibration of Roadway Traffic ........................................................................ 15

Figure 4: Validation of Roadway Travel Times ............................................................... 16

Figure 5: Validation of Transit Travel Times (Southbound) ............................................ 17

Figure 6: Validation of Transit Travel Times (Northbound) ............................................ 18

Figure 7: Distribution of Lateness and Early Arrivals (Southbound) ............................... 19

Figure 8: Distribution of Lateness and Early Arrivals (Northbound) ............................... 19

Figure 9: LRT Reference Points in Study Network .......................................................... 22

Figure 10: Simulation of LRT Trajectories in Analytical Model ..................................... 24

Figure 11: Duration of Blockage Event ............................................................................ 27

Figure 12: Validation of Search Based Optimization Tool for Dwell Time ..................... 31

Figure 13: Validation of Search Based Optimization Tool for Roadway Stopped Delay 32

Figure 14: Layout Of LRT References Point In Study Area ............................................ 34

Figure 15: Simulated LRT Strategies ............................................................................... 36

Figure 16: Overall Person Delay for Different Train Strategies on 1300S....................... 39

Figure 17: Overall Person Delay for Different Train Strategies on 2100S....................... 40

x

Figure 18: Person Delay at Crossing on 1300S for Different LRT Strategies on

Same Crossing .................................................................................................44

Figure 19: Impact of Priority Strategy on 1300S .............................................................. 46

Figure 20: Person Delay at Crossing on 2100S for Different LRT Strategies on

Same Crossing .................................................................................................50

Figure 21: Impact of Priority Strategy on 2100S .............................................................. 51

1

1 INTRODUCTION

According to the Transportation Research Board’s Committee on Light Rail Transit,

Light Rail Transit (LRT) is defined as “a metropolitan electric railway system

characterized by its ability to operate single cars or short trains along exclusive rights of

way at ground level, on aerial structures, in subways or, occasionally, in streets, and to

board and discharge passengers at track or car-floor level”. (1) With its lower

implementation cost than metro and comparable high-capacity LRT is often seen as an

affordable and efficient railway transit option which provides an alternative to the private

transportation. At the same time, LRT represents a competitive mode to private

transportation at conflict points in the network. At those points, train operations should be

defined in such a way to provide smooth most efficient operations for both LRT and

roadway traffic.

Several priority strategies can be implemented into the control plan for an at-grade

crossing. (2) These strategies can range from an unconditional priority (preemption) at all

times for LRT vehicles to a situation in which LRT vehicles must wait for an acceptable

gap in the traffic stream. From the perspective of transit services, preemption is a better

choice because it maximizes transit service reliability and quality of service by totally

eliminating transit delay (3). However, preemption causes additional delay to vehicular

traffic and pedestrians at LRT crossings. Analytical computations of these delays cannot

be normally encountered in traffic engineering analysis. Non-cyclical and directional

2

nature of LRT arrivals renders traditional intersections and network analysis technique

inappropriate. (4)

Regardless to the complexity of delay computations, literature and current practice

suggest person delay as a measure of effectiveness (MOE) which will provide a method

of associating a quantifiable user cost with the operation of an LRT system with at grade

crossings.

1.1 Problem Statement

Person delay as a representative measure of effectiveness at light rail transit crossing

defines the average lost time per “user” while he/she is passing LRT crossing by either

private car or transit. Preemption defines no-delay for LRT passengers and causes extra

delay for private cars while the other priority strategies provide more green time for

private cars and introduce delay for LRT vehicles. Different train strategies bring the

different amount of delays for both private car and LRT. Therefore, person delay is also

different for different train strategies.

The other factor, which affects the person delay at LRT crossing, is train schedule.

Train schedules usually propose constant headway and unique offset time. Headway

represents amount of time between two consecutive departures from same station and

direction. Offset time defines the time between two consecutive train departures from

opposite directions. Train offset suggests the point in the network where trains from

opposite directions suppose to “meet”. If trains arrive at a crossing simultaneously, the

impact on private traffic (for same priority strategy) is much less than if they arrive at

different times. Furthermore, if one of LRT vehicles arrives immediately after another

3

(from opposite directions), the overall impact on private traffic may be much greater than

for separate arrivals.

The problem that needs to be addressed may be formulated as: What combinations

of train priority and train schedule for given traffic and transit volume is going to bring a

minimal overall person delay? In order to bring a minimal values, each possible

combinations of train priority and schedule has to be observed. This kind of problem can

not be efficiently addressed through micro-simulation. Building and analyzing of each

possible scenario in micro-simulation represent computationally intensive and expensive

process.

1.2 Research Goals and Objectives

This study searches for set of train priority and schedule, that brings a minimal

overall person delay in case study area. The goal of this study is to develop analytical

model, which will be able to extract combination of train priority and train schedule to

minimize overall person delay at three LRT crossings at case study area. The objective of

the study is to develop micro-simulation model of study area, which will provide a set of

input parameters for the analytical model, and through validation process defines strength

and weaknesses of analytical model. This was achieved through one case study example

in Salt Lake City, UT.

1.3 Thesis Organization

This thesis consists of seven chapters. The following chapter gives an overview of

light rail transit operations and analytical computations of vehicular delay at railroad

4

crossing. Chapter three describes the microsimulation model that is used in this study. It

includes the modeling process, calibration and validation of the model, and a description

of future basic scenario, which was built for the validation purpose of analytical model.

Chapter four describes analytical model. It defines analytical calculations of vehicular,

transit and person delay, validation of analytical model as well as some limitations which

were found during building process. Chapter five provides and analyses results obtained

using analytical model in case study area. Chapter six provide discusion about final

output and major limitations in analytical model. Chapter seven summarizes major

conclusions of study and identifies the areas for future research.

5

2 LITERATURE REVIEW

The primary goal of this research is to develop analytical model, which provides a

LRT strategy that minimizes person delay at LRT crossing. Simulation of Light Rail

operations and calculation of person delay without using any microsimulation traffic

software have represented challenging job. However, previous studies and research

significantly alleviated this duty. This chapter gives a brief overview of LRT impact on

private traffic as well as methodology for computational traffic delay at LRT crossing.

2.1 Light Rail Operations

Several studies were conducted in the past to quantify effects of LRT operations on

vehicular traffic. Chalander and Hoel, investigated the effects of light rail services on

average delays experienced by vehicular traffic. (1) They used the VISSIM computer

simulation model to test four scenarios with light rail crossings: isolated crossings of two-

lane and four-lane roads, a case in which light rail transit is located in the median of a

street, and a larger network that includes four crossings. For different variations of

vehicular and transit volumes, they investigated additional delay experienced by vehicles

due to LRT services. For isolated crossings of two/four lane roads they found that

average additional delays caused by LRT vehicle increased with the frequency of LRT

operations and the growth in vehicular volumes

6

James Cline, in his Master of Science Thesis, examined the delays of vehicular

traffic at LRT crossings caused by LRT service. (5) NETSIM computer simulation model

was used for testing four scenarios with light rail crossings: an isolated crossing, an

adjacent intersection crossing, a series of coordinated intersections with preemption, and

a case study based on a corridor in Houston. He found that the major factor in the

vehicular traffic delay, experienced by LRT service, was a volume to capacity (v/c) ratio.

Nelson and Bullock (6) examined the impact of emergency vehicle preemption on

closely spaced arterial traffic signals through seven preemption paths and three different

preemption times. They found that a single preemption call had a minimal effect on the

overall travel time and delay while multiple preemption call causes serious queuing and

delay problems. In addition, the impact of multiple preemption calls is more severe if

they are next to each other.

Bullock et al. (7) analyzed impact of emergency vehicle traffic signal preemption on

travel time and delay of traffic on a signalized corridor in Northern Virginia during the

morning rush hour. In their findings they emphasized impact of cycle transition

parameters on the controller’s ability to recover from preemption.

Gerken and Tracy (8) evaluated LRT impact on vehicular traffic through vehicular

delay and queue length at an existing isolated intersection in Union County, New Jersey.

They simulated and evaluated traffic operations at an intersection which is 254 feet away

from the railroad crossing. Their findings showed that frequent LRT service caused

additional delay for the tangent direction of tracks, while LRT service will have no

impact on the parallel direction of tracks.

7

Li et al. (9) described a concept and the implementation of LRT using an active

priority system for highway/rail grade crossing. The major part of active priority system

represents a priority request generator which adopts a three-scheme conditional priority

control strategy. Schemes are designed according to the train schedule adherence. The

concept was tested on a case study for a San Diego Trolley system and it showed

significant savings.

Ekeila et al. (10) compared conventional and dynamic Transit Signal Priority (TSP)

systems in two case studies - a hypothetical intersection and a proposed light rail

corridor. Simulations’ results showed that dynamic TSP system was better than the

conventional system.

Faran (11) provided an overview of innovative pedestrian and motor vehicle traffic

control designs and practices that had been applied to LRT in Barcelona, Spain. Tian et

al. (12) mathematically described a relationship between schedule-delay cost function

and in-vehicle congestion cost function. They found that concavity and convexity

characteristics of the in-vehicle congestion cost function and the schedule delay cost

function should be opposite.

Wadjas and Furth (13) used Vehicle Actuated Programming (VAP) logic in VISSIM

to develop a control strategy based on advanced prediction which provides passage with

near-zero delay for transit vehicles with negligible impact on the other traffic. They

conducted simulations on Massachusetts’ Huntington Avenue corridor in Boston, which

is served by a light rail line. Their results showed that 82% of the trains arrived during the

green phase which caused substantial improvements to transit travel time with little

impact on other traffic.

8

2.2 Computation of Roadway Delay at Railroad Crossing

Delays of vehicular traffic caused by train service at LRT crossing cannot be

normally encountered in traffic engineering analysis as a consequence of non-cyclical

LRT arrivals. In order to resolve this problem Walter Okitsu developed a model for free

LRT grade crossing delay. (14)

In order to provide quick and cheap estimation of traffic delay at LRT crossing,

caused by freight passage, commuter rail and Amtrak service Okitsu collected field data

and developed a model. During 24-hour video recording at 33 crossings in Los Angeles

County’s San Gabriel Valley, the behavior of traffic signals and the private traffic were

observed for each blockage event. Simple isolated crossings to complex crossings with

preempted traffic signals on one or both sides were observed in the study area. Frequency

of the train service occurs from 10 up to 80 times per day at the same locations while the

durations of crossing blockages ranged from a few seconds to 53 minutes.

By observing recorded field condition for each crossing and for each direction, Okitsu

defined a relationship between vehicular flow characteristics (arrival and saturation flow

rate, delay time) and total vehicular delay at LRT crossings, experienced by train service.

Okitcu’s formula [1] uses duration of each blockage event (B) and vehicular flow

characteristics at LRT crossing to estimate total vehicular delay (D) at railroad crossing

caused by LRT service. Vehicular flow characteristics such as arrival rate (AR),

saturation flow rate (S) and lost time (LT) have been quantified by observing field data.

9

2*( )

2*(1 )

AR B LTD

ARS

[1]

The total vehicular delay is calculated for each blockage event. The total daily

vehicular delay is the summation of these vehicular delays calculations throughout the

day. Authors didn’t have opportunity to calibrate and validate their calculation model.

Rymer at al. (15) tried to estimate vehicular delay as a function of crossing-volume to

capacity ratio (Xcr). Through NETSIM microsimulation software, they simulated LRT

grade crossing operations for different roadway cross section, vehicular and transit

volumes, and different clearance times. Cross-section varied from two to six lines.

Volume ranged from 250 vehicles to 1000 vehicles per hour per lane. LRT headway

varied from 2.5 to 12.5 min which corresponds tofive t o twenty-four LRT interruptions

during one hour. Crossing clearance times of 30, 40 and 50 seconds were tested.

They found that crossing-volume-to-capacity ratio (Xcr) is inversely proportional to

the time available for vehicular crossing time (g) and directly proportional to the

demand/saturation ratio (v/s) [2]. The vehicular crossing time (g) decreases as lost time

and LRT crossing time increase, which in turn penalizes the operational capacity of the

roadway segment.

1( ) ( )crvX

g s [2]

Vehicular crossing time (g) represents a portion of time available for the vehicular

traffic to cross the tracks. This time is calculated for known LRT headway (C), LRT

crossing clearance time (CCT) and lost time (L) [3].

10

( )C CCT Lg

C

[3]

During their research, they showed how clearance time and LRT headways have an

impact on vehicular delay. While either clearance time or LRT headways increases,

vehicular traffic delay tends to increase, too. As a final output, they defined a dependence

of vehicular delay (d) on crossing-volume to capacity ratio (Xcr) [4]

(sec/ ) 91.16 crd veh X [4]

In their estimation of vehicular delay, authors neglected the randomness in train

clearance time and train departure time.

Although some authors (14,15) developed a methodology for estimating vehicular

delay at LRT crossing, they didn’t have opportunity to test and validate their models.

Furthermore, they didn’t try to extract the most efficient LRT strategy. This study tried to

fill this gap. Analytical model was developed, validated and run to provide strategy that

minimizes person delay at LRT crossings in case study area.

11

3 NETWORK SIMULATION MODEL

This chapter describes a case study microsimulation model, which was built to

provide necessary data for building and validation of the analytical model. Case study

area is located in Salt Lake City and microsimulation model refers to projected 2015 year

when number of trains which traveling in study area will be significantly increased. Train

strategy for 2015 should be extracted through analytical model. .

3.1 Case Study Area

In order to satisfy estimated ridership in future years, Utah Transit Authority is going

to increase Light Rail Service in Salt Lake City. This extension in spatial coverage and

frequency will bring greater potential for operational conflicts with private cars. Segment

between crossings at 1300S and 2100S is chosen as the most critical part for projected

2015. Along this most-frequent LRT segment, expected number of trains will reach 26

trains per hour which represents a significant increase compared to the current 12 trains

per hour. LRT stations, which are located in vicinity the of LRT crossings, additionally

increase an impact on vehicular operations at crossing on 1300S and 2100S. Figure 1

shows the case study network as well as locations of LRT station.

12

Figure 1: Case Study Area

3.2 Modeling process

Microsimulation software VISSIM 5.2 (16) was an efficient and user-friendly tool in

modeling vehicular and transit operations in the case study network. Vehicle Actuated

Programming (VAP) platform within VISSIM significantly alleviates coding signal

timing preemption.

The study case network was modeled in a VISSIM simulation software, with the

existing network geometry, traffic volumes, turning movements at intersections, signal

timing data, and transit operations for the PM peak period from 4:00 PM to 6:00 PM.The

study area network was converted to the VISSIM’s link-connector model from the

VISUM UT State network model. Converted model was checked and corrected by

13

observing Google Earth. Figure 2 shows the modeled VISSIM geometry of case study

area.

Figure 2: VISSIM Model of Study Area

Modeled VISSIM geometry was loaded with traffic volumes provided from different

sources. Traffic volumes on arterial streets were estimated according to the Annual

Average Daily Traffic for 2008 and 2009 . Those data can be found on Utah Department

Of Transportation (UDOT) website. Traffic volumes on I15 ramps were found on UDOT

Performance Measurement System (PeMS) platform. Traffic counts for two intersections

(for 2008) were provided by UDOT while for the rest of the network, traffic counts were

estimated by using Excel balancing spreadsheet. Traffic signals were provided (as PDF

files) by UDOT. Those PDFs files were manually imported into the VISSIM’s NEMA

platforms for each individual controller.

14

LRT tracks in the study area with stations on 1300 South and 2100 South were coded

by observing Google maps and Google earth. Extensions of tracks on both side (south

and north) were modeled to accommodate dummy stations. Those stations emulate

lateness and early arrivals from the field. Additionally, future spatial extension of LRT

tracks was modeled according to arterial maps.

LRT segment was loaded with train departures according to the current Utah Transit

Authority (UTA) schedule. These departures were offset by certain intervals by creating

dummy stations right at the entering points. Dwell times on regular station, as well as

deviations in scheduled arrivals, were extracted from provided GPS train travel times

data. Those values were imported in VISSIM as empirical distributions. Each of those

empirical distributions is defined by its extreme value (min and max) and sets of

intermediate points with their belonging probability. Occupancy of LRT vehicle for each

line and direction was found in the current UTA ridership.

Preemption at railroad crossings was set-up according to UTA’ instructions.

Locations of check in and check-out detectors for each crossing as well as necessary

changing time from one stage to another (LRT to vehicular and vice versa) were given by

UTA. According to the UTA instruction:

“Once the train crosses the track circuit, the flashers on the gates begin and flash

for about 4 seconds, then the gates drop which takes about 3 seconds”

“The gates remain down until the last train vehicle passes a track circuit located

approximately 80 feet past the crossing. The gates then take about 7 seconds to

rise. Only then can auto traffic pass.”

15

3.3 Calibration and Validation of VISSIM Model

Calibration and validation of VISSIM model were performed for private and LRT

transit separately. This chapter provides analysis and results of this process.

3.3.1 Vehicular Data

Provided Traffic counts for signalized intersections and ramps were used to calibrate

traffic operations in the model. VISSIM was programmed to collect the same data

through 10 random seed simulations. Figure 2 shows high correlation between data sets

collected in the field and those from the simulation.

R² = 0.993

0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800 1000 1200 1400 1600

Model t

raff

ic c

ounts

[veh/h

]

Field traffic counts [veh/h]

Figure 3: Calibration of Roadway Traffic

16

Private traffic operations in the model were validated for travel times. Field travel

times were collected at four major intersections during PM peak hours during the week of

February 17th

,2010. Through floating-car technique, travel times were recorded using

GPS devices and laptops.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Tra

vele

d d

ista

nce [ft

]

Time [s]

Travel Time Runs on 1700S WB

Field travel runs VISSIM travel runs

9%

2%

5%

Figure 4: Validation of Roadway Travel Times

Only trajectories of vehicles from simulation, whose routes are identical with those

of field vehicles were observed and included in validation process. Figure 3 (which refers

to 1700S WB travel time segment) shows such a travel time profile for one travel time

segment and percentage of vehicles (in microsimulation) whose travel time is similar

(within ± 10%) to the time of the vehicles in the field .The number (percentage) attached

to each activity shows how many percent of vehicles in the microsimulation (traveling on

17

the same segment and having the same origin and destination points) experience a very

similar activity.

3.3.2 Transit Data

GPS travel times of LRT vehicles were used to validate transit operations in the

study area. Travel times of the LRT vehicles were provided (by UTA) in a format that

included both travel times between two consecutive LRT stops and dwell time at the

arriving (second) LRT stop. VISSIM was programmed to collect the same data through

10 random seed simulations. Figures 4 and 5 show how accurately the VISSIM model

replicates travel times and dwell times at LRT stations near 1300S and 2100S.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

<135 135-145 145-155 155-165 165+

Rela

tive fre

quency

Travel time (including dwell time) [sec]

FIELD

VISSIM

Figure 5: Validation of Transit Travel Times (Southbound)

18

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

<135 135-145 145-155 155-165 165+

Rela

tive fre

quency

Travel time (including dwell time) [sec]

Field

VISSIM

Figure 6: Validation of Transit Travel Times (Northbound)

Furthermore, train schedule deviations from the field were validated. Train

deviations represent important part of LRT operations and through introducing dummy

stations at the entrance points in the network, those deviations were modeled. If early and

late arrivals in the microsimulation did not resemble those from the field this then the

evaluation of various schedule scenarios would not provide trustworthy results. Field and

simulation deviations from the scheduled train arrivals are shown in Figures 6 and 7.

These figures show that VISSIM can simulate lateness and early arrivals of LRT trains

from the field and emulate LRT schedule adherence from the field.

19

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-120 - 0 0 - 120 120 - 240 240 - 360 360+

Re

lative

fre

que

ncy

Deviations from scheduled arrival [sec]

Field

VISSIM

Figure 7: Distribution of Lateness and Early Arrivals (Southbound)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-80 - -20 -20 - 40 40 - 100 100 - 160 160 - 220 220 - 280 280+

Re

lative

fre

que

ncy

Deviations from scheduled arrival [sec]

Field

VISSIM

Figure 8: Distribution of Lateness and Early Arrivals (Northbound)

20

3.4 Future Operations

One future scenario was built in a properly calibrated and validated model according

to the future traffic and transit operations for projected 2015.

Traffic volumes were inflated according to the estimated volumes for 2015.

Future traffic data were estimated according to the traffic demand for 2030 which

was provided by Wasatch Front Regional Council from their long range

transportation plan.

Transit volumes for 2015 are defined according to the UTA long-term plan. In the

study area network, UTA proposes 26 trains per PM peak hour (14 in southbound

and 12 in northbound direction). In the future basic scenario, trains from the

opposite directions simultaneously enter the network.

New dwell times on regular stations were estimated according to the current and

future ridership. Ratio between the future and current ridership was multiplied by

a current dwell time in order to estimate future dwell time.

Current and future headways were used to estimate future train scheduled arrival

deviations. Future deviations will be smaller as a consequence of more frequent

LRT operations.

The purpose of this scenario is to alleviate building of analytical model and to provide

input parameters for the future validation process of the analytical model. Train logic of

this scenario invokes preemption at all LRT crossings and a train schedule which

proposes simultaneous train departures from the opposite directions (offset 0).

21

4 ANALYTICAL MODEL

The purpose of analytical model is to calculate vehicular and transit delay for

different combinations of train schedule and train priority in order to bring transit strategy

which minimizes overall person delay at three isolated LRT crossings in study area. Idea

behind this model is to build and simulate LRT trajectories which resemble those from

the field and for given traffic, transit and signal timing data calculate traffic, transit and

person delay. Through one automatic and iterative process, train schedules and priority

were changed and tested.

4.1 Simulation of Train Trajectories

Train trajectories were simulated in the MS Excel spreadsheet using a set of

normally distributed random numbers and time space diagrams of LRT vehicles. Train

trajectories define the sets of times when train arrives at, departures from, or just passes

reference points in the network. Reference points in train trajectories represent points on

the LRT tracks which are important for modeling transit and traffic signal operations at

LRT crossings. These points are shown on Figure 9 and they are:

Entrance point in the network

Dummy station which was built to simulate lateness and early arrivals of

trains

22

Regular station in the network

Check in and check-out detectors for LRT crossings.

Figure 9: LRT Reference Points in Study Network

Normally distributed random numbers are introduced to simulate different travel

time between each two reference points as well as different dwell times of LRT vehicles

on regular and dummy stations. Those deviations can be found in LRT time space

23

diagrams. Time-space diagram of LRT vehicles can be extracted from either Global

Positioning System (GPS) data of LRT vehicles or microsimulation model (if one exist)

which is able to provide LRT trajectories as an output.

In this study, analytical model was built to extracts a best LRT strategy for projected

2015.Only source, which can be used to extract train trajectories in this case, is VISSIM

model. Future scenario was built to alleviate building of analytical model by providing

necessary data. Ten simulation runs of VISSIM model provided sample data of 260 train

trajectories in south bound and 240 train trajectories in north bound.

Distributions of dwell time on regular/dummy stations as well as travel time

distributions between each pair of references points were extracted from VISSIM

trajectories files and transformed into normal distributions with parameters µi and δi.

Figures 10 shows parameters for SB directions which were found in VISSIM future

model. Furthermore, figure 10 gives the Y-coordinates of reference points on the LRT

tracks and explains the role of normally distributed random numbers in calculation of

time when train pass across reference point. Dwell time at station on 1300S (cell H7 –

cell H6) is defined as normally distributed value with mean of 46.56 seconds (cell B7)

and standard deviation of 15.1 seconds (cell C7). VISSIM output trajectories of LRT

vehicles also show that dwell time at station on 1300S doesn’t exceed 70 seconds and

doesn’t take values which are smaller than 7 seconds. The same restrictions were

simulated in analytical model (formula bar).

24

Figure 10: Simulation of LRT Trajectories in Analytical Model

In simulation traffic and transit operation at LRT crossings, very important role plays

activation of traffic signal on these crossings. Activation of traffic signal is defined by

time when train activates a check in detector and amount of delayed time (if any exists)

which is introduced to simulate different priority strategies. This amount of time

represents a delayed activation of traffic signal and it can range from 0 which correspond

to preemption strategy up to same maximum value. This maximum value is defined as a

maximum dwell time at corresponding LRT station.

. During the observation of the VISSIM simulation, simultaneous passing trains across

LRT crossing were recorded. During these situations, one train activates traffic signal

while the other deactivates traffic signal and finished train phase. Additionally, on the

LRT crossings near regular stations it was recorded that one train (which is dwelling)

activates and deactivates traffic signal while the train from the opposite direction is

served. Those situations were also found in an Excel simulation of train trajectories.

25

In order to extract and chronologically define times of activation and deactivation of

traffic signals, Visual Basic for Applications procedure was written. This procedure

simulates traffic signal operation from the field and clearly defines the starts and

terminations of train and car phases. Instruction from the field, regarded to traffic signal

and gate operations were included in this procedure.

As a final output of the this step, the time value for each reference point of each train

trajectories are defined. Furthermore, activation and deactivation of traffic signal were

calculated .Train trajectories are simulated for both directions during the whole

simulation period.

4.2 Calculation Vehicular, Transit and Person Delay

In previous step, LRT trajectories were simulated and exact activations and

deactivations of traffic signals were provided. Those times provided sets of durations of

vehicular and transit phases. Duration of those phases have an impact on vehicular,

transit and person delay.

The other parameters which are necessary for calculation of vehicular, transit and

person delay are shown in Table 1 and these parameters were provided from VISSIM

future scenario output.

26

Table 1: Recorded Parameters in VISSIM Simulation

Vehicular, Transit and

Signal Timing Characteristics

LRT Crossing

1300S 1700S 2100S

Veh

icula

r tr

affi

c Arrival rate (veh/hour) WB 1244 587 867

Arrival rate (veh/hour) EB 1289 569 755

Saturation flow rate (veh/hour) 3600 3600 3600

Average occupancy (per/car) 1.3 1.3 1.3

Lost time (s) 0 0 0

Amber - flash (s) 4 4 4

LR

T

Arrival rate (veh/PM period)SB 26 26 26

Arrival rate (veh/PM period)NB 24 24 24

Ave. occupancy (pax/train) SB 348 348 348

Ave. occupancy (pax/train) NB 320 320 320

Gates drop (s) 3 3 3

Gates rise (s) 7 7 7

4.2.1 Vehicular Delay

Vehicular delay at LRT crossing in analytical model was calculated using Okitcy

formula from literature.[5] Okitcu formula uses duration of each blockage event (B) and

vehicular flow characteristics at LRT crossing to estimate total vehicular delay (D) for

each crossing and direction caused by LRT services. Average vehicular delay was

calculated by dividing total vehicular delay (D) with corresponding arrival rate.

* *( )

2

AR Q B LTD

……

1 ( / )

B LTQ

AR S

… [5]

D - Total vehicular delay (hours) AR - Arrival flow rate (veh/hours)

LT - Lost Time (hours) S - Saturation flow rate (veh/hours)

B – Duration of blockage event

27

Arrival and saturation flow rate as well as lost time were extracted from VISSIM

future scenario (Table 1). Duration of each blockage event was calculated by known

activation and deactivation of traffic signals at LRT crossings, flashing time and time

which gates take to rise up. Flashing and rise up time were found in both field and

VISSIM future model while time of activation and deactivation traffic signals were

provided in LRT trajectories. Figure 11 shows how duration of blockage event was

calculated. Calculation of blockage event and vehicular delay were calculated for each

crossing and each direction separately.

Figure 11: Duration of Blockage Event

4.2.2 Light Rail Transit Delay

Light rail transit delay represents the average delay which LRT vehicle and its

passengers experience while they traverse across light rail crossing. Delay time doesn’t

include dwell time at regular and dummy station. In addition, in order to alleviate both

comparison of different transit strategies and calculation of transit delay, acceleration and

deceleration lost times were neglected. These constant times don’t have any impact on

final decision.

28

Analytical model defines a light rail transit delay as average amount of time which

LRT passenger spend waiting to get right of way. LRT trains and its passengers can

experience this delay on stations which are located between check-in detector and LRT

crossing. On these stations, it can be recorded that train finishes boarding and alighting

passengers but still doesn’t have right of way. Those situations are related to conditional

preemption which was codded by delayed activation of traffic signals on LRT crossing. If

preemption is deployed on the LRT crossing, there is no delay for LRT vehicles. Delay of

LRT vehicles for the cases when conditional preemption is deployed in the field is

calculated from LRT trajectories according formula:

( )LRT d tp fD T T T

Td - Time when train passes across check-out detector (sec)

Ttp - Travel time between station and check-out detector when preemption is

deployed (sec)

Tf - Time when train is ready to leave a station (sec)

Previous formula shows that LRT delay is calculated as a difference between times

when train leaves a station (Td-Ttp) and time when train is ready to leave (Tf). This delay

was calculated for each crossing and direction separately.

4.2.3 Person Delay

The major goal of analytical model is to provide strategy which minimizes overall

person delay in study area. Person delay can be calculated for known volumes,

occupancies and average delays for both transportation modes on LRT crossings. Traffic

29

and transit volumes as well as average occupancy per car/train were provided by future

VISSIM scenario, while previous steps provided calculations of vehicular and LRT

delay. Arrival rates for each arterial street and direction as well as average occupancy of

LRT and cars were found in output data of VISIM model for 2015 (Table 1). Person

delay on particular crossing and overall person delay in study area network are calculated

according following formulas [6] and [7]:

/ / / //

car EB EB car WB WB LRT SB SB LRT NB NBp cr

EB WB SB NB

D P D P D P D Pd

P P P P

[6]

/ / / /

1/

1

i i i i i i i i

i i i i

n

car EB EB car WB WB t SB SB t NB NB

ip area n

EB WB SB NB

i

D P D P D P D P

d

P P P P

[7]

Where:

dp/c - average person delay per crossing

dp/area - overall person delay for n crossing in study network

- Average delay for transportation mode x which traveling in YZ direction

(sec/person)

- Number of persons who traveling in YZ direction

4.3 Validation of Analytical Model

Analytical model of case study area was validated for LRT dwell times and vehicular

delay at LRT crossings. Dwell times on regular and dummy stations were chosen

because their stochasticity and it was important to show that analytical model is capable

30

of emulating randomness in train departures and train dwell time from the field or

VISSIM model.

Dwell times on regular and dummy stations were extracted from train trajectories

through quite simple computational process. Reference point which represent train

arrivals at dummy/regular station were subtracted from reference point marked as train

departures for same dummy/regular station on the same train trajectory.

Through iterative process, dwell times for each train trajectory were extracted and

sample of data was provided. Mean values and standard deviations from this sample data

were compared to corresponding VISSIM outputs. Figure 12 shows results of those

comparisons and prove that analytical model is capable of precisely simulating train

trajectories from the field and field randomness in these trajectories.

31

0

20

40

60

80

100

120

140

160

180

DummyStation SB

DummyStation NB

Station on1300S SB

Station on1300S NB

Station on2100 SB

Station on2100 NB

Dw

ell T

ime [

sec]

Station

Microsimulation Model

Analytical Model

Figure 12: Validation of Search Based Optimization Tool for Dwell Time

Another parameter which was validated is vehicular delay at LRT crossing.

Vehicular delay in analytical model was provided as a final output of Okitcy formula

while in microsimulation this parameter was extracted as one of the VISSIM output

results. Vehicular delay was provided for each crossing and direction. Comparison of

corresponding roadway delays at railroad crossings is shown on Figure 15.

32

0

5

10

15

20

25

30

35

1300S WB 1300S EB 1700S WB 1700S EB 2100S WB 2100S EB

Dela

y [

sec/v

eh

]

Crossing & Direction

Microsimulation Model

Analytical Model

Figure 13: Validation of Search Based Optimization Tool for Roadway Stopped Delay

Figure 13 shows that the only disagreement between analytical and microsimulation

simulation model can be found on crossing on 1300S for west bound direction. This

crossing cannot be observed as a fully isolated, because queued vehicles at downstream

traffic signal exceed LRT crossing. Mentioned traffic signal on intersection 1300S and

300W is the most critical signal in the network, with highest traffic volumes. Green time

over cycle length ratio for west bound and eastbound direction is 0.3. The ratio on traffic

signal, which precedes LRT grading on 1300S for westbound direction, is significantly

bigger - 0.7.

Slightly different directional vehicular volumes at LRT crossing on 1300S (Table 1)

and identical vehicular green time at LRT crossing should produce a similar delay for

33

eastbound and westbound direction. However, downstream traffic signal causes extra

delay for westbound direction at LRT crossing on 1300S. As figure 10 shows, analytical

model is capable of estimating delay on isolated LRT crossing while extra delay, caused

by nearby traffic signal, cannot be estimated using this tool.

4.4 Simulation of Different Train Strategies

Analytical model calculates overall person delay for different combinations of train

schedule and train priority at LRT crossing. Through one incremental and iterative

process, input parameters such as train schedule and train priority were offset and tested.

Different train schedules were tested by changing the departure times from one

direction with 15 seconds of incremental step. Projected headway for 2015 is five

minutes or 300 seconds what brings 20 different train schedules. Those train schedules

were combined with different priority strategies in study area.

Priority strategies were defined by observing layout of LRT reference points in study

area network . According , LRT layout from the field it was found that:

Different priority strategies should be tested at LRT crossing on 1300S for

southbound direction and at LRT crossing on 2100S for northbound

direction. In these cases, regular station is located between check-in and

check-out detectors for corresponding crossing and dwell time on those

stations has impact on vehicular operations (Figure 12)

Dwell time on regular stations on 1300S for northbound direction and on

2100S for southbound direction doesn’t have impact on vehicular operations

on LRT crossing. These stations are located behind corresponding check-out

34

detectors (Figure 12) and as a consequence, LRT preemption is kept for these

approaches.

There is no regular station in vicinity of grading 1700S. (Figure 12)

Consequently, there is no sense to implement any other priority on this

crossing except currently deployed preemption logic, which provide more

efficient operation for both transportation modes.

Figure 14: Layout Of LRT References Point In Study Area

35

The impact of different LRT’ priority on overall person delay is simulated through

delayed activation of traffic signal on 1300S SB and 2100S NB. Delayed activation

varied from 0 to maximum dwell time with incremental step of 10 seconds. Maximum

dwell times at station on 1300S and 2100S NB are 70 sec and 50 seconds respectively.

4.5 Limitations of Analytical Model

Analytical model was built to test all possible combinations of train schedules and

train priorities and to provide a minimal overall delay in case study area. In this particular

study area there are two LRT crossings (1300S and 2100S) where different priority

strategies should be simultaneously tested. These priorities are simulated by introducing

delayed activation of traffic signals on LRT crossing. Ten seconds increment of delayed

activation of traffic signal for maximum dwell time of 70/50 seconds on station on 1300S

SB/2100S NB provide in total 48 different combinations. Furthermore, those 48 different

combinations should be tested for 20 different train schedules. This is going to bring a

960 combination of different LRT strategies.

Unfortunately, MS excel is not capable of simulating delayed activation of traffic

signals (conditional preemption) at two or more different LRT crossings, simultaneously.

Excel warns that formula refers to the cell in which it is contained, either directly or

indirectly and stops the further executions. In order to mitigate and partially resolve this

problem simulation of conditional preemptions at different crossings were modeled

separately for station 1300S SB and 2100S NB.

Figure 11 shows variety of train schedules and transit priority which were changed

and tested through analytical model. Two sub-scenarios were modeled in order to

36

separately perform simulations of different transit priorities at LRT crossings on 1300S

and 2100S in study area network.

Figure 15: Simulated LRT Strategies

.

37

5 RESULTS AND ANALYSIS

This chapter provides results obtained from analytical model. Analytical model

estimated a delay for different combinations of train schedules and delayed activation of

traffic signal on either 1300S SB or 2100S NB. Each combination of input parameters

was simulated for PM peak period through ten random seeds. Analytical model was set-

up to calculate and extract overall person delay for different combinations of train

schedule and train priority.

Analytical model is not able to simultaneously emulate conditional preemption

strategies on two or more LRT crossings. Because of mentioned limitation, two sub-

scenarios were modeled. In each of them, different delayed activation of traffic signal

were changed at only one LRT crossing while preemption was deployed at others LRT

crossings in the network. Results are organized on such a way to show impact of train

schedules and different priority strategies on overall person delay. Furthermore, impact of

train strategies on person delay were observed on that crossing where strategies were

changed and tested.

38

5.1 Impact of Different Train Schedules on Overall Person Delay

Different train schedules were tested through changing departure times for one

direction with constant incremental steps of 15 seconds. Extracted overall person delays

for different offsets in train schedule are shown in Table 2. Table 2 shows statistics (mean

and standard deviation) for overall person delay for each of the train schedules when

preemption was deployed at all crossings. Hypotheses that mean values of various

performance measures are equal was tested. T-test for means and paired samples were

used, with 95% confidence level. The results show that train schedule with offset of 270

seconds is significantly better than the other seventeen train schedules.

Table 2: Overall Person Delay for Different Train Strategies

Overall person delay

offset0 9.96 (0.91)

offset15 9.93 (0.59)

offset30 9.98 (0.38)

offset45 10.10 (0.79)

offset60 9.65 (0.43)

offset75 9.37 (0.33)

offset90 9.94 (0.65)

offset105 9.45 (0.38)

offset120 9.35 (0.45)

offset135 9.68 (0.44)

offset150 9.56 (0.43)

offset165 9.37 (0.40)

offset180 9.36 (0.50)

offset195 9.28 (0.58)

offset210 9.07 (0.47)^

offset225 9.80 (0.87)

offset240 9.27 (0.62)

offset255 9.39 (0.74)

offset270 8.78 (0.39)

offset285 8.93 (0.54)^

offset300 9.86 (0.49)

^ value is not significantly different from corresponding offset 270 value

39

Schedule of 270 seconds doesn’t represent a best solution only for the case when

preemption is deployed at all crossing. Figures 18 and 19 show overall person delay for

different train schedules and priority strategies on LRT crossing on 1300S (Figure 18)

and 2100S (Figure 19). Those figures show that there is no unique offset value which

generates the minimal overall person delay for each priority strategies on 1300S/2100S.

However, from those figures can be seen that values of minimal overall person delay for

different train strategies on 1300S or 2100S are clustered around offsets of 270 and 285

seconds.

4

5

6

7

8

9

10

11

12

13

14

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300

Ove

rall

Pe

rso

n D

ela

y i

n S

tud

y A

rea

Train Schedule Offset (sec)

Preemtion at all crossings

Delayed activation of signal on 1300S for 10 sec

Delayed activation of signal on 1300S for 20 sec

Delayed activation of signal on 1300S for 30 sec

Delayed activation of signal on 1300S for 40 sec

Figure 16: Overall Person Delay for Different Train Strategies on 1300S

40

8

8.5

9

9.5

10

10.5

11

11.5

12

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300

Ove

rall

Pe

rso

n D

ela

y i

n S

tud

y A

rea

Train Schedule Offset (sec)

Preemtion at all crossings

Delayed activation of signal on 2100S for 10 sec

Delayed activation of signal on 2100S for 20 sec

Delayed activation of signal on 2100S for 30 sec

Delayed activation of signal on 2100S for 40 sec

Figure 17: Overall Person Delay for Different Train Strategies on 2100S

5.2 Impact of Different LRT Priority Strategies

Different train priorities were simulated by changing delayed activation of traffic

signal on crossing 1300S and 2100S separately from zero to maximum dwell time for

corresponding station with 10 seconds incremental step. Impact of different priority

strategies was observed on overall person delay as well as on person delay on that

crossing where priority strategies where changed and tested. Furthermore, graph and

statistical interpretations of results was provided for person delay on particular crossings.

41

5.2.1 Different LRT Priorities at Crossing on 1300S SB

Impact of different LRT priorities on 1300S was observed on overall person delay in

study area and person delay on crossing at 1300S. Delayed activation of signal on 1300S

was changed from 0 to maximum dwell time with 10 seconds incremental steps while the

preemption was kept on crossings 1700S and 2100S. Maximum dwell time at station on

1300S is 70 seconds what brings eight different priority strategies on 1300S. Overall

person delay as well as person, vehicular and LRT person on crossing 1300S were

calculated.

Table 3 shows overall person delay for all combination of train schedules and train

priorities on 1300S SB. Results show that the minimal overall delay can extracted by

strategy which defines train schedule offset of 285 seconds and delayed activation of

traffic signal on 1300S of 30 seconds. Again, additional improvement is possible to

achieve by simultaneously changing priority strategy on 2100S which can not be model

in analytical model.

42

Table 3: Overall Person Delay for Different LRT Strategies on 1300S

Delayed Activation of Traffic Signal on 1300S SB 0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec

Offset 0 9.96

(0.91) 8.74

(0.55) 8.09

(0.40) 7.34

(0.57) 7.02

(0.55) 7.19

(0.36) 8.60

(1.26) 9.22

(0.17)

Offset 15 9.93

(0.59) 8.75

(0.47) 8.02

(0.29) 7.25

(0.32) 7.35

(0.86) 7.03

(0.43) 7.85

(0.49) 8.68

(0.71)

Offset 30 9.98

(0.38) 8.66

(0.62) 8.01

(0.47) 7.41

(0.36) 7.20

(0.44) 7.28

(0.52) 7.83

(0.35) 8.48

(0.56)

Offset 45 10.1

(0.79) 8.76

(0.51) 7.89

(0.38) 7.37

(0.49) 6.97

(0.36) 7.15

(0.54) 7.69

(0.65) 8.63

(0.45)

Offset 60 9.65

(0.43) 8.90

(0.53) 7.96

(0.38) 7.37

(0.52) 7.11

(0.36) 7.27

(0.38) 7.97

(0.82) 8.70

(0.77)

Offset 75 9.37

(0.33) 8.47

(0.39) 7.96

(0.45) 7.61

(0.33) 7.21

(0.37) 7.39

(0.51) 7.76

(0.53) 8.62

(0.85)

Offset 90 9.94

(0.65) 8.53

(0.50) 7.94

(0.40) 7.32

(0.40) 7.34

(0.46) 7.35

(0.54) 7.67

(0.55) 8.07

(0.57)

Offset 105 9.45

(0.38) 8.47

(0.27) 8.05

(0.26) 7.51

(0.34) 7.40

(0.53) 7.62

(0.50) 7.79

(0.67) 8.58

(0.54)

Offset 120 9.35

(0.45) 8.82

(0.57) 7.61

(0.36) 7.69

(0.45) 7.23

(0.44) 7.76

(0.58) 7.83

(0.75) 8.49

(0.65)

Offset 135 9.68

(0.44) 8.62

(0.46) 7.67

(0.60) 7.23

(0.35) 7.23

(0.39) 7.21

(0.77) 7.50

(0.54) 8.45

(1.03)

Offset 150 9.56

(0.43) 8.48

(0.41) 7.71

(0.53) 7.59

(0.53) 7.26

(0.54) 7.10

(0.35) 7.86

(0.48) 9.16

(0.41)

Offset 165 9.37

(0.40) 8.35

(0.59) 7.89

(0.62) 7.27

(0.71) 7.03

(0.59) 6.93

(0.56) 7.85

(0.42) 9.08

(0.62)

Offset 180 9.36 (0.50

8.31 (0.61)

7.46 (0.47)

7.06 (0.48)

7.08 (0.64)

7.00 (0.38)

7.76 (0.44)

9.05 (0.67)

Offset 195 9.28

(0.58) 8.58

(0.58) 7.68

(0.32) 7.19

(0.61) 6.87

(0.66) 7.06

(0.72) 7.90

(0.74) 8.98

(0.59)

Offset 210 9.07

(0.47) 8.27

(0.46) 7.64

(0.51) 6.80

(0.43) 7.06

(0.70) 7.07

(0.45) 8.26

(0.79) 9.29

(0.56)

Offset 225 9.80

(0.87) 8.21

(0.38) 7.20

(0.52) 7.10

(0.42) 6.66

(0.40) 6.85

(0.57) 7.80

(0.51) 9.09

(0.90)

Offset 240 9.27

(0.62) 7.88

(0.38) 7.48

(0.38) 7.14

(0.60) 6.64

(0.52) 7.11

(0.63) 7.90

(0.39) 9.01

(0.59)

Offset 255 9.39

(0.74) 8.06

(0.50) 7.19

(0.46) 6.97

(0.82) 6.57

(0.39) 6.95

(0.53) 7.54

(0.58) 8.63

(0.60)

Offset 270 8.78

(0.39) 8.00

(0.51) 7.45

(0.90) 6.54

(0.41) 6.43

(0.42) 6.77

(0.46) 7.76

(0.46) 8.94

(0.77)

Offset 285 8.93

(0.54) 8.03

(0.56) 7.14

(0.38) 6.42

(0.34) 6.52

(0.46) 6.87

(0.52) 7.46

(0.62) 8.88

(0.59)

Offset 300 9.86

(0.49) 8.97

(0.40) 7.94

(0.41) 7.19

(0.34) 7.36

(0.82) 7.15

(0.34) 8.34

(0.73) 9.24

(0.48)

Table 4 shows the person delay at crossing on 1300S for different combinations of

train schedule and delayed activation on traffic signal on 1300S. Table 4 shows that the

minimal person delay at 1300S can be achieved by train schedule of 270 seconds and

delayed activation of traffic signal on 1300S of 30 seconds. Graphical interpretation of

results from table 4 is given on Figure 18.

43

Table 4: Person Delay at Crossing on 1300S for Different Strategies on Same Crossing Delayed Activation of Traffic Signal on 1300S SB

0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec

Offset 0 9.88

(1.21) 8.15

(0.84) 7.23

(0.60) 6.05

(0.88) 5.60

(0.74) 5.87

(0.49) 7.92

(1.79) 8.91

(0.34)

Offset 15 9.92

(0.87) 8.21

(0.65) 7.01

(0.55) 5.96

(0.50) 6.06

(1.04) 5.77

(0.73) 6.87

(0.55) 8.23

(1.03)

Offset 30 10.02 (0.62)

7.98 (0.94)

7.05 (0.73)

6.37 (0.59)

5.84 (0.57)

5.97 (0.78)

6.94 (0.49)

7.99 (0.85)

Offset 45 10.33 (1.25)

8.27 (0.77)

7.13 (0.52)

6.15 (0.63)

5.51 (0.69)

6.07 (0.82)

6.78 (1.02)

8.03 (0.67)

Offset 60 9.84

(0.64) 8.54

(0.84) 7.30

(0.50) 6.34

(0.60) 6.00

(0.39) 6.12

(0.62) 7.27

(1.34) 8.27

(1.16)

Offset 75 9.36

(0.49) 7.94 (0.5)

7.30 (0.68)

6.78 (0.54)

6.07 (0.43)

6.55 (0.59)

7.11 (0.76)

8.28 (1.14)

Offset 90 10.22 (0.90)

8.27 (0.62)

7.30 (0.58)

6.36 (0.56)

6.44 (0.69)

6.48 (0.8)

7.00 (0.74)

7.65 (0.75)

Offset 105 9.72

(0.58) 8.09

(0.36) 7.63

(0.42) 6.66

(0.47) 6.41

(0.63) 6.98

(0.50) 7.18

(0.94) 8.42

(0.67)

Offset 120 9.54

(0.49) 8.63

(0.57) 7.15

(0.55) 7.03

(0.57) 6.43

(0.59) 7.10

(0.86) 7.20

(1.07) 8.37

(0.93)

Offset 135 10.03 (0.51)

8.49 (0.46)

7.23 (0.66)

6.37 (0.50)

6.34 (0.66)

6.43 (0.99)

6.98 (0.84)

8.10 (1.47)

Offset 150 9.73

(0.58) 8.20

(0.62) 7.26

(0.62) 7.03

(0.88) 6.62

(0.62) 6.29

(0.40) 7.37

(0.67) 9.20

(0.60)

Offset 165 9.49

(0.36) 8.15

(0.64) 7.34

(0.81) 6.42

(0.97) 6.1

(0.87) 6.05

(0.87) 7.42

(0.51) 9.04

(0.77)

Offset 180 9.59

(0.64) 7.86

(0.74) 6.65

(0.51) 6.25

(0.45) 6.14

(0.95) 6.25

(0.62) 7.32

(0.59) 9.01

(0.98)

Offset 195 9.5

(0.79) 8.54

(0.75) 7.00

(0.56) 6.06

(1.00) 5.9

(0.78) 6.3

(0.99) 7.33

(1.22) 8.78

(0.88)

Offset 210 8.94

(0.51) 7.78

(0.61) 6.83

(0.60) 5.93

(0.55) 5.71

(0.74) 6.3

(0.38) 7.95

(1.00) 9.15

(0.73)

Offset 225 9.48

(0.86) 7.75

(0.61) 6.4

(0.91) 5.94

(0.58) 5.49

(0.49) 5.9

(0.69) 7.06

(0.76) 9.01

(1.03)

Offset 240 9.19

(0.78) 7.34

(0.64) 6.47

(0.64) 6.03

(0.57) 5.36

(0.66) 6.02

(0.88) 7.33

(0.39) 8.72

(0.79)

Offset 255 9.08

(0.68) 7.21

(0.49) 6.19 (0.5)

5.40 (0.29)

5.21 (0.52)

5.83 (0.58)

6.77 (0.65)

8.34 (0.93)

Offset 270 8.38

(0.63) 7.31

(0.38) 6.23

(0.56) 5.02

(0.40) 5.20

(0.50) 5.43

(0.58) 6.71

(0.52) 8.84

(1.08)

Offset 285 8.64

(0.77) 7.04

(0.31) 5.92

(0.42) 5.08

(0.29) 5.08

(0.57) 5.34

(0.46) 6.63

(0.83) 8.28

(0.79)

Offset 300 9.75

(0.67) 8.39

(0.62) 7.02

(0.54) 5.89

(0.44) 6.02

(1.02) 5.75

(0.59) 7.55

(0.99) 8.78

(0.71)

44

Figure 18: Person Delay at Crossing on 1300S for Different LRT Strategies on Same Crossing

Strategies in blue area generate better results than those in any other colored area.

One of these strategies should be deployed in the field. Strategies from red zones

generate the worst results and according figures these strategies refer to preemption.

Statistical analysis was performed for person delay on 1300S. Train priorities were

changed on 1300S and it is very important to show how these changes impacted a person

delay on same crossing. Table 5 shows a significance of results from Table 4 where

symbol “X” refers to strategies which extract significantly different person delay on

1300S than the best strategy. Symbol “O” belongs to strategy which extracts not

significantly different person delay on 1300S than the best strategy. Bolded “O”

represents best strategy and it can be found for delayed activation of traffic signal of 30

seconds and train schedule with offset of 270 seconds. Table 5 shows that 7 train

strategies provide results which are not significantly different from those which are

generated by best train strategy.

45

Table 5: Significance of Results for Different Priority Strategies on 1300S Delayed Activation of Check-in Detector on 1300S SB

0 sec 10 sec 20 sec 30 sec 40 sec 50 sec 60 sec 70 sec

Offset 0 X X X X X X X X Offset 15 X X X X X X X X Offset 30 X X X X X X X X Offset 45 X X X X X X X X Offset 60 X X X X X X X X Offset 75 X X X X X X X X Offset 90 X X X X X X X X

Offset 105 X X X X X X X X Offset 120 X X X X X X X X

Offset 135 X X X X X X X X Offset 150 X X X X X X X X

Offset 165 X X X X X X X X Offset 180 X X X X X X X X Offset 195 X X X X X X X X Offset 210 X X X X X X X X Offset 225 X X X X X X X X

Offset 240 X X X X O X X X Offset 255 X X X X O X X X

Offset 270 X X X O O O X X

Offset 285 X X X O O O X X

Offset 300 X X X X X X X X

The impact of different train strategies on 1300S on person delay at same crossing

can be easily seen on Figure 18. This figure shows vehicular, transit and person delay at

crossing on 1300S for different priority strategies and train schedule offset of 270

seconds. By increasing delayed activation of traffic signal, vehicular delay is going to

decrease because of smaller amount of red time, while at the same time LRT delay tends

to increase. Person delay at crossing on 1300S decreases simultaneously with increasing

activation delayed time up to 30 seconds. After this point, with further increasing delayed

46

activation, person delay tends to increase. Minimal person delay are achieved for 30

seconds of delayed activation.

LRT delay represents average delay for LRT trains ant their passengers. LRT trains,

which traverse in northbound direction, always have a full preemption at crossing on

1300S and their passengers travel without any delay on this crossing. However, LRT

passengers who traverse in southbound direction are faced with delay because of

conditional preemption at LRT crossing on 1300S and this delay is greater than average

LRT delay.

0

5

10

15

20

25

0 10 20 30 40 50 60 70

Dela

y a

t C

rossin

g o

n 1

300S

Delayed Activation of signal on 1300S SB

Vehicular

Person

Light Rail Transit

Figure 19: Impact of Priority Strategy on 1300S

47

5.2.2 Different LRT Priorities at Crossing on 2100S NB

Impact of train’s priority at crossing on 2100S was done on identical way as for

crossing on 1300S. Delayed activation of traffic signals on 2100S was changed from zero

up to maximum dwell time (50 sec) with incremental 10 seconds steps. Six different

priority strategies on 2100S were combined with different train schedules in order to

estimate vehicular, transit and person delay in study area and at LRT crossing on 2100S.

Table 6 shows overall person delay for all combination of train schedules and train

priorities on 2100S SB. During those simulations, preemption was kept on 1300S and

1700S.If preemption is deployed on 1300S and 1700S then minimal overall delay in

study area can extracted by strategy which defines train schedule offset of 285 seconds

and delayed activation of traffic signal on 2100S of 20 seconds. It is interesting to

conclude that identical train schedule offset (285 seconds) generates best results in two

subscenarios.

48

Table 6: Overall Person Delay for Different LRT Strategies on 2100S

Delayed Activation of traffic signal on 2100S

0 sec 10 sec 20 sec 30 sec 40 sec 50 sec

Offset 0 9.96 (0.91) 9.60 (0.62) 9.69 (1.40) 9.70 (0.40) 11.04 (0.90) 11.97 (1.12)

Offset 15 9.93 (0.59) 9.66 (0.59) 9.54 (0.56) 9.70 (0.53) 10.30 (0.37) 12.60 (1.14)

Offset 30 9.98 (0.38) 9.66 (0.50) 9.58 (0.78) 9.53 (0.50) 10.58 (0.42) 12.12 (0.71)

Offset 45 10.10 (0.79) 9.34 (0.28) 9.42 (0.35) 9.88 (0.65) 10.70 (0.59) 11.88 (0.97)

Offset 60 9.65 (0.43) 9.46 (0.50) 9.43 (0.52) 9.61 (0.39) 10.40 (0.43) 11.88 (0.75)

Offset 75 9.37 (0.33) 8.99 (0.70) 9.15 (0.51) 9.68 (0.82) 10.19 (0.64) 11.66 (0.91)

Offset 90 9.94 (0.65) 9.66 (0.65) 9.62 (0.6) 9.63 (0.75) 10.29 (0.61) 11.62 (0.74)

Offset 105 9.45 (0.38) 9.29 (0.48) 9.29 (0.46) 9.47 (0.51) 10.47 (0.68) 11.48 (0.42)

Offset 120 9.35 (0.45) 9.24 (0.55) 9.21 (0.41) 9.3 (0.38) 10.37 (0.59) 11.35 (0.74)

Offset 135 9.68 (0.44) 9.00 (0.66) 9.04 (0.45) 9.21 (0.50) 10.26 (0.74) 11.03 (0.69)

Offset 150 9.56 (0.43) 9.16 (0.58) 9.27 (0.64) 9.21 (0.74) 10.07 (0.44) 11.25 (0.55)

Offset 165 9.37 (0.40) 9.30 (0.68) 9.01 (0.66) 9.28 (0.48) 10.06 (0.6) 10.67 (0.59)

Offset 180 9.36 (0.50 9.48 (0.75) 8.95 (0.60) 9.34 (0.53) 9.95 (0.51) 10.44 (0.72)

Offset 195 9.28 (0.58) 8.90 (0.61) 8.94 (0.52) 9.36 (0.42) 9.80 (0.76) 10.77 (0.70)

Offset 210 9.07 (0.47) 9.08 (0.67) 8.71 (0.40) 9.14 (0.81) 9.61 (0.53) 10.87 (0.83)

Offset 225 9.80 (0.87) 8.97 (0.52) 8.53 (0.50) 8.75 (0.47) 9.83 (0.74) 10.82 (0.76)

Offset 240 9.27 (0.62) 8.64 (0.38) 8.29 (0.44) 8.67 (0.59) 9.54 (0.8) 10.97 (0.95)

Offset 255 9.39 (0.74) 9.00 (0.85) 8.68 (0.64) 8.97 (0.68) 9.80 (0.49) 10.69 (0.61)

Offset 270 8.78 (0.39) 8.52 (0.53) 8.54 (0.58) 8.90 (0.79) 10.01 (0.52) 10.42 (0.46)

Offset 285 8.93 (0.54) 8.46 (0.41) 8.27 (0.45) 8.73 (0.47) 9.96 (0.44) 10.83 (0.64)

Offset 300 9.86 (0.49) 9.81 (0.80) 9.45 (0.70) 9.71 (0.47) 10.53 (0.37) 11.98 (0.56)

Table 7 shows the person delay at crossing on 2100S for different combinations of

train schedule and delayed activation on traffic signal on 2100S. Train schedule offset of

180 seconds and delayed activation of traffic signal on 2100s of 20 seconds brings the

minimal person delay at LRT crossing on 2100S if preemption is deployed at other LRT

crossings. Figure 19 shows graphical interpretation of results from table while table 8

shows a significance of results in table 7.

49

Table 7: Person Delay at Crossing on 2100S for Different Strategies on Same Crossing

Delayed Activation of traffic signal on 2100S

0 sec 10 sec 20 sec 30 sec 40 sec 50 sec

Offset 0 4.46 (0.36) 3.54 (0.23) 3.32 (0.21) 3.81 (0.37) 5.58 (0.55) 7.65 (0.76)

Offset 15 4.41 (0.38) 3.51 (0.23) 3.42 (0.27) 3.97 (0.3) 5.40 (0.68) 7.99 (0.58)

Offset 30 4.24 (0.27) 3.4 (0.22) 3.31 (0.25) 3.96 (0.42) 5.40 (0.62) 7.76 (0.53)

Offset 45 4.29 (0.21) 3.4 (0.16) 3.19 (0.12) 3.8 (0.4) 5.42 (0.44) 7.68 (0.89)

Offset 60 4.07 (0.22) 3.44 (0.19) 3.05 (0.17) 3.77 (0.41) 5.22 (0.72) 7.76 (0.62)

Offset 75 3.94 (0.24) 3.32 (0.17) 3.12 (0.2) 3.74 (0.35) 5.05 (0.54) 7.19 (0.73)

Offset 90 4.00 (0.38) 3.30 (0.26) 3.01 (0.13) 3.72 (0.38) 5.08 (0.42) 6.8 (1.43)

Offset 105 3.76 (0.22) 3.16 (0.34) 3.01 (0.29) 3.57 (0.48) 5.14 (0.68) 6.99 (0.99)

Offset 120 3.68 (0.24) 3.35 (0.27) 3.05 (0.30) 3.75 (0.62) 5.00 (0.58) 7.02 (0.94)

Offset 135 3.94 (0.50) 3.09 (0.18) 3.07 (0.47) 3.58 (0.53) 4.81 (0.84) 6.41 (0.86)

Offset 150 3.78 (0.4) 3.38 (0.67) 3.24 (0.57) 3.39 (0.43) 4.73 (0.45) 6.45 (0.73)

Offset 165 3.85 (0.75) 3.49 (0.79) 3.13 (0.68) 3.74 (0.58) 4.82 (0.88) 6.52 (1.23)

Offset 180 4.07 (0.56) 3.66 (0.91) 2.88 (0.62) 3.51 (0.56) 4.61 (0.57) 5.72 (1.16)

Offset 195 3.63 (0.26) 3.40 (0.53) 3.21 (0.67) 3.59 (0.8) 4.51 (0.94) 6.26 (0.67)

Offset 210 3.83 (0.47) 3.33 (0.64) 3.01 (0.32) 3.82 (0.87) 4.56 (0.50) 6.52 (1.65)

Offset 225 4.05 (0.48) 3.48 (0.70) 3.01 (0.49) 3.49 (0.46) 5.08 (0.88) 6.27 (0.99)

Offset 240 3.94 (0.52) 3.21 (0.34) 2.95 (0.32) 3.32 (0.56) 4.88 (0.88) 6.95 (1.22)

Offset 255 3.88 (0.43) 3.79 (0.99) 3.16 (0.71) 3.79 (0.38) 5.07 (0.81) 6.91 (0.99)

Offset 270 3.89 (0.21) 3.21 (0.14) 3.04 (0.44) 3.96 (0.74) 5.02 (0.6) 6.88 (0.81)

Offset 285 3.82 (0.24) 3.38 (0.54) 2.99 (0.5) 3.67 (0.67) 5.60 (0.62) 7.32 (0.84)

Offset 300 4.45 (0.20) 3.50 (0.20) 3.27 (0.29) 4.00 (0.43) 5.67 (0.35) 7.90 (0.66)

50

0 5 10 15 20 25 30 35 40 45 500

100

200

300

2

3

4

5

6

7

8

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Delay Activation on Signal on 2100S NB (sec)

Train

Schedule Offset

(sec)

Per

son D

elay

(se

c)

Figure 20: Person Delay at Crossing on 2100S for Different LRT Strategies on Same Crossing

Table 8: Significance of Results for Different Priority Strategies on 1300S Delayed Activation of traffic signal on 2100S 0 sec 10 sec 20 sec 30 sec 40 sec 50 sec

Offset 0 X X X X X X

Offset 15 X X X X X X

Offset 30 X X O X X X

Offset 45 X X O X X X

Offset 60 X X O X X X

Offset 75 X X O X X X

Offset 90 X X O X X X

Offset 105 X O O X X X

Offset 120 X O O X X X

Offset 135 X O O X X X

Offset 150 X O O X X X

Offset 165 X O O X X X

Offset 180 X X O X X X

Offset 195 X O O X X X

Offset 210 X O O X X X

Offset 225 X X O X X X

Offset 240 X X O X X X

Offset 255 X X O X X X

Offset 270 X O O X X X

Offset 285 X O O X X X

Offset 300 X X O X X X

51

Same as in previous case, impact of different priority strategies can be clearly seen at

Figure 21. This figure shows vehicular, transit and person delay at crossing on 2100S for

different priority strategies and train schedule offset of 270 seconds. By 20 seconds of

delayed activation of traffic signal on 2100S, minimal person delay can be provided on

this crossing.

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45 50

Dela

y a

t C

rossin

g o

n 2

100S

Delayed Activation of Signal on 2100S NB

Vehicular

Person

Light Rail Transit

Figure 21: Impact of Priority Strategy on 2100S

52

5.3 Person Delay Savings

Analytical model tests different train strategies in order to find which one brings the

minimal overall person delay. Previous results shows that minimal person delay is

possible to achieve by introducing some amount of delay time on check-in detectors.

Those amounts of times are 30 seconds and 20 seconds for check-in detectors on 1300S

SB and 2100S NB, respectively for schedule offset of 270 seconds. Benefits of this

strategy can be quantified through monetary savings on annual basis.

As a consequence of tool’ incapability of simulating delays at check-in detectors on

different grading simultaneously, monetary savings were performed for each crossing

separately. Person savings are observed separately for LRT crossings on 1300S and

2100S by comparing minimal person delay per crossing for non-preemption and

preemption strategy. The best non-preemption strategy proposes a schedule offset of 270

seconds and delayed activation of 30 and 20 seconds on LRT crossings on 1300S and

2100S respectively. This strategy produces person delay of 5.02 seconds at crossing

1300S (Table 4) and 3.04 seconds of person delay at crossing on 2100S. (Table 7) The

best preemption strategy is achieved for train schedule offset of 270 seconds and this

strategy generates a person delays of 8.38 and 3.89 seconds at LRT crossing on 1300S

and 2100S, separately.

In first step, total number of persons who travel across LRT crossing by either

private car or light rail transit was calculated. Table 9 shows number of persons per

approach, transportation mode as well as total number of persons.

53

Table 9: Person Demand at LRT Crossings

Vehicular Traffic Light Rail Transit

EB WB SB NB

1300S

PM peak volumes 2576 2488 26 24

Ave. occupancy (person/car) 1.3 1.3 348 320

Persons 3349 3234 9048 7680

Persons (per mode) 6583 16728

Persons (Total) 23311

2100S

PM peak volumes 1610 1734 26 24

Ave. occupancy (person/car) 1.3 1.3 348 320

Persons 2093 2254 9048 7680

Persons (per mode) 4347 16728

Persons (Total) 21075

Table 10 shows person delay for strategy which is currently deployed in the field

(full preemption) as well for strategy extracted from analytical model. Furthermore,

Table 5 shows time savings per person and total savings per LRT crossing for PM peak

period. Finally, total savings at LRT crossings in network is equal to 27.17 person*hours

per PM peak period. It is important to repeat that these savings were estimated according

person delays at particular crossing, which were simulated in two separated sub scenarios

and obviously this way doesn’t represent best way of compering different strategies for

overall person delay in study area.

Table 10: Saving Time at LRT Crossing

Grading Volumes

(persons/PM)

Person Stopped Delay

(sec/per) Savings

(second)

Total savings

(person*hour) Preemption

Proposed

scenario

1300S 23311 8.38 5.02 3.36 21.76

2100S 21075 3.89 3.04 0.85 4.98

Total NA NA NA 26.74

54

Monetary savings are calculated by multiplication saved person hours with average

cost of time. Those savings refer to PM peak period for workday. Table 11 shows that

these values ranged between ~ $400.00 and ~$800.00 (forth row) for three different

values of times obtained from various US DOT and Urban Mobility studies. Table 6 also

show that annual overall benefits are ranged between ~$100,000 and ~$200,000.

Table 11: PM and Annual Overall Benefits

Urban Mobility and US DOT Values of Time

Cost per hour $14.60 $20.00 $30.00

Hours of delay

time 26.74 26.74 26.74

Dollars of time

in delay $390.40 $534.80 $802.20

Number of work

days per year 250 250 250

TOTAL $97,601.00 $133,700.00 $200,550.00

Time savings are quantified for LRT crossings during PM peak period. Impact of

different train strategies on roadway operation at nearby traffic signals cannot be

observed and further quantified. Quantifying time savings during off PM peak period

wasn’t possible to achieve because of unavailability of vehicular and transit delay.

55

6 DISCUSSION

Analytical model was built to extract a strategy which minimizes overall person

delay in study area. Some limitations, which still can’t be resolved, restricted the

performance of this task. Analytical model defines a strategy which brings a minimal

person delay at particular crossing if preemption is deployed on others LRT crossing.

Furthermore, analytical model show that minimal person delay at LRT crossing is

possible to achieve by introducing delayed activation of traffic signal (on that side where

station precedes to LRT crossing). This amount of delay depends of estimated vehicular

and transit volumes as well as dwell time on station which precedes to LRT crossing. The

major benefit of this model should be its capability of re-running for different sets of

traffic and transit volumes and different dwell time parameters on regular and dummy

station. On that way, potential wrong estimation of traffic and transit data for 2015 can be

easily corrected.

Traffic and transit volumes can be collected in field. Dwell time at regular station as

well as deviations in train schedule can be found in future GPS data. Train technical

characteristics as well as safety requirements at LRT crossing can be changed in future

years. Any of these changes (if any happens) can be on fast and cheap way addressed in

analytical model. Furthermore, impact of this wrong estimation can be seen and

analytical model can be re-run to extract a best strategy for new data on each LRT

56

crossing, separately. Although analytical model can not simulate different train strategies

on two or more LRT crossings at same time, this model shows impact of different LRT

strategies on vehicular and transit operations on particular crossing. By simulating a wide

range of possible combination, analytical model give as a wide picture of potential future

operation and shows how LRT operations should be codded to provide the highest

benefit.

Person delay savings were done to estimate future savings for given vehicular and

transit data. Although, best strategy can not be simulated through analytical model, with

high level of confidence we can claim that proposed strategy will bring significantly

better results in field then currently deployed preemption strategy. This strategy could be

provided without using any microsimulation software. Again, VISSIM model provided

necessary data only for validation of analytical model.

57

7 CONCLUSIONS AND FUTURE RECOMMENDATIONS

The goal of this study was to develop analytical model which will be able to estimate

person delay for different LRT schedules and priorities, and extract strategy to minimize

overall person delay at LRT crossings. Building and validation of analytical model was

done and explained through one case study example. In this case study, trains which

traverse in north-south direction disrupt vehicular operations at three LRT crossings.

Location of transit station in study area additionally affects vehicular operations on

particular crossing. Dwell times of southbound trains at station on 1300S and northbound

trains on 2100S affect duration of “gate-down” time on corresponding crossing. Impact

of LRT dwell time on vehicular traffic accompanied with different train schedule was

estimated for projected 2015 when transit volumes will significantly increase. This was

done through one analytical model, which was adopted for case study in Salt Lake City.

Analytical model simulated train operations for different combinations of train

schedule and priority strategies on those crossing where station’ dwell time affects

vehicular operations. Furthermore, this model estimates person delay at LRT crossing for

each transit strategy. Finally, this model, through one searching process, extracts strategy

which brings minimal person delay on particular crossing if preemption is deployed on

other crossings. Person or user delay was chosen as a representative measures of

effectiveness (MOE) because at the same time invokes a vehicular and transit delay.

58

The following conclusions were reached in this study during building and validation

analytical model.

Analytical model is capable of simulating train trajectories from the field.

Randomness in station dwell time and deviations in train schedule and train travel

times are simulated using normally distributed random numbers. Distributions

behind those random numbers were provided from VISSIM model which

simulated train and vehicular operations for 2015.

Analytical model can estimate vehicular delay at isolated LRT crossings.

Through automatized calculation process, based on Okitcy formula, analytical

model calculates a vehicular delay at isolated crossing. Traffic characteristics data

such as vehicular volumes and crossing signal parameters have to be known.

Analytical model brings a strategy, which minimize person delay on

particular crossing. Although this model was purposely made to find a strategy,

which minimizes an overall person delay, some limitations during building

process restrict this intense. However, analytical model can extracts strategy

which minimize person delay at particular LRT crossing. Through one

incremental-iterative process, different transit strategies were simulated and

tested. Results were compared and the best of simulated strategy was provided.

Impact of near traffic signal cannot be observed by analytical model.

Analytical model simulates train operations. Vehicular operations are defined by

vehicular volumes and LRT crossing signal parameters. Different patterns in

vehicular arrivals as well as vehicular operations at nearby traffic signals can not

be simulated using this model.

59

This model is not capable of simultaneously simulating different train

strategies at two or more LRT crossings. MS Excel cannot perform a logic

behind simultaneously simulation priority strategies on two or more LRT

crossings. In this case study, problem was partially overcome by separately

simulation priority strategies on two LRT crossings.

Analytical model was run for particular case study in Salt Lake City (UT). Additional

conclusions were reached for this study.

Train schedule with offset of 270 seconds provide best results for currently

deployed preemption at all LRT crossings. Results show that schedule offset of

270 seconds provides significantly better results than other 17 out of 19 train

schedules, if preemption is deployed at all crossings.

By increasing delayed activation of traffic signal, vehicular delay is going to

decrease while LRT delay is going to increase. Delayed activation of traffic

signal assigns more green time for vehicular traffic while at the same time

introduce potential delay for transit vehicles and their passengers. Solution, which

provides minimal sum of total vehicular and transit delay was searched by

analytical model.

It is estimated that between $100,000.00 and $200,000.00 can be saved per

year if best scenario (generated from analytical model) is used instead of the

currently deployed preemption. These savings do not represent real money but

are monetary equivalents of (reduced) delays experienced by all users of the

system during PM period. These savings reflect only PM peak period operations

60

and further analysis is necessary to investigate if off-peak operations offset or

further increase these savings.

Analytical model represents one innovative approach in simulation transit operations

without using any simulation traffic software. Although described VISSIM model was

used in building and validation search based tool, this source of data can be replaced by

GPS LRT data and field observation. The benefit of this model is providing cheap and

fast answer on question what is going to happened in future years if particular train

strategy would be deployed in the field. Broad ranges of transit strategy which can be

simulated through this tool at the same time represent the major advantage in compare to

simulation traffic softwares. However, this model can not provide wide range of

measures of effectiveness. This model was intentionally made as an additional tool to

alleviate set-up particular input parameters in microsimulation software. In order to avoid

tuning of some VISSIM input parameters this tool was run. Final output of analytical

model show values for mentioned input parameters.

Limited performance of analytical model should be investigated and improved in the

future. Simulation impact of nearby traffic signals as well as simultaneously simulations

of different train priority at two or more railroad grading should be addressed in the

future years.

61

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