Traffic Assignment Convergence and its Effects on Selecting Network Improvements By Chris Blaschuk,...

Traffic Assignment Traffic Assignment Convergence and its Convergence and its Effects on Selecting Effects on Selecting

Network ImprovementsNetwork Improvements

By

Chris Blaschuk, City of Calgary

and

JD Hunt, University of Calgary

October 20, 2004

18th Annual International EMME/2 User’s Conference

Mexico City, Mexico

OutlineOutline• About the Calgary Regional Transportation Model• Multiclass Assignment Process and Algorithms• Project Evaluation Process and Issues• Project Evaluation Measures

– Mobility Benefits– Vehicle Hours Traveled (VHT)

• Empirical Testing– Candidate Projects– Observations

• Results of Testing• Conclusions

City of CalgaryCity of Calgary• Population just over 1 million people

Calgary RTMCalgary RTM• Both city and surrounding

region modeled• Consists of 1447 zones

and over 14000 links• 24-Hour model broken

into five time periods• System of logit choice

models• 25 trip purposes• 5 person types

75km

24 Hour Trip Destination Choice:

j(2)

origin z one i

j(n)....j(1)

des tination z one j

Time of Day Choice:

am off

da ily i-j

pm

Mode Choice:

car1 car2 car3

car p&r

trans it auto

mechanica l

cy cle

metabo lic

wa lk

time o f day i-j

Peak Crown vs Peak Shoulder Choice:

peak crown

car mode i-j

peak s houlder

Figure 2: Conceptual nested logit model structure

Calgary RTMCalgary RTM• Steep VDF Curves used

– Links not overloaded– Forces changes in generation, distribution and mode split

Multiclass Assignment in RTMMulticlass Assignment in RTM• Generalized cost multiclass

assignment is used in the Calgary RTM.

• Five classes assigned simultaneously.

• Truck penalty on non-truck routes for medium and heavy trucks.

• Stored as extra attribute of fixed link costs for these classes.

• Originally was 1000 min / 250 meters for skimming -- now is 5 min / 100 meters.

Using RTM in Project EvaluationUsing RTM in Project Evaluation• 34 separate projects to be tested for network benefits• These included

– Road Widenings

– Interchanges

– Lane Reversal Systems

– New Roadways

– Some Bundles of the above

• Goal was to determine the benefit each improvement on the network in order to decide where money should be invested.

• Wanted to use ‘Mobility Benefits’

Mobility BenefitsMobility Benefits• Change in daily

composite utility by model segment

• Equal to change in traveler consumer surplus

• Indicates benefits of changes to person types and trip types

• Useful for analyzing transit and other mode improvements as well as network changes.

Generalized Cost of Travel

Link Volumes

Demand Curve for Network Links

0 V1 V2

C1

C2

Consumer Surplus

Problem with ResultsProblem with Results• Got confusing results

– Lots of unexpected negative benefits– Results were not intuitive– Unacceptable - clearly something wrong

• Needed to investigate– decided on assignment convergence

• Approach: isolate problem– fixed trip table– considered just VHT– examine assignment process– experiment with convergence criteria

Reasons for Approach Reasons for Approach • Simplify to auto network• Eliminated ‘induced demand’• Simple to understand• Results more certain, more predictable• Smaller, so quick to produce and process• Observe assignment convergence effects

Empirical TestingEmpirical Testing• Two projects were tested at various levels of

convergence• Effects observed included

– Fluctuation of volumes on links– Time taken to conduct assignment– VHT of network at said level of convergence

Empirical TestingEmpirical Testing• Project 1: John Laurie Boulevard widening from

Sarcee Trail to 53 ST NW (4 to 6 Lanes):– Simple widening, impact generally limited to peak periods

only.– Network effects are more local than far-reaching.

Empirical TestingEmpirical Testing• Project 2: Glenmore Trail widening from Crowchild

Trail to 14 ST SW (7 to 10 Lanes):– Major East-West corridor, important link in network.– Network effects are far-reaching with no close alternative

routes.

Empirical Testing ObservationsEmpirical Testing Observations• Volume Fluctuation on Links would occur in areas

where travel times were very close. – “Flip-Flopping” would occur -- case when two scenarios are

compared, an amount of volume takes path A in one scenario and path B in another.

– More of a concern in the offpeak period than peak periods.

Empirical Testing ObservationsEmpirical Testing Observations• Fixed Link Costs affect

assignment convergence and time. – Used in Commercial Vehicle

Model to represent non-truck routes (penalty applied to links)

– Increased fixed link costs cause the multiclass assignment to think it has converged quickly when it has not.

Number of Iterations for VariousTruck Penalty Costs

Relative Gap (%)Truck Penaltyper 100 meters

0.01 0

1 48 -2 49 -3 48 5775 44 41410 41 21140 32 -80 28 -200 20 -450 19 39

- Not Tested

ResultsResultsJohn Laurie Boulevard Widening Project

TABLE 2: Assignment Statistics for John Laurie Boulevard Widening, AM Crown Case1

Relative Gap (%)0.10 0.05 0.04 0.03 0.02 0.01 ~0 2

Iterations 212 315 358 428 580 907 2000Computing Time (h) 1.25 1.85 2.11 2.52 3.40 5.35 11.72Maximum/MinimumVolume Difference3

18.54-15.59

13.38-9.31

7.69-6.28

7.08-5.43

4.47-3.08

2.94-2.66

1.11-0.81

Vehicle Hours Traveled 82917 82897 82895 82895 82897 82896 828961 For a truck trip penalty of 5 minutes per 100 meters.2 A maximum of 2000 iterations was used as a stopping criteria.

3 Difference in volume links from previous iteration for the last iteration in the assignment.

TABLE 3: Assignment Statistics for John Laurie Boulevard Widening, AM Shoulder CaseRelative Gap (%)

0.10 0.05 0.04 0.03 0.02 0.01 ~0Iterations 90 131 150 180 216 341 2000Computing Time (h) 0.54 0.78 0.90 1.08 1.29 2.03 11.84Maximum/MinimumVolume Difference

61.68-36.96

27.49-23.79

31.55-15.60

15.29-11.60

10.05-11.57

6.06-3.80

0.72-0.61

Vehicle Hours Traveled 62269 62242 62224 62228 62229 62217 62214

ResultsResultsGlenmore Trail Widening Project

TABLE 4: Assignment Statistics for Glenmore Trail Widening, AM Crown CaseRelative Gap (%)


19.38-14.07

9.61-11.25

10.86-10.27

4.67-4.85

6.03-3.11

2.81-2.34

1.01-0.86


TABLE 5: Assignment Statistics for Glenmore Trail Widening, AM Shoulder CaseRelative Gap (%)


47.20-30.48

19.52-30.66

17.08-16.88

13.95-13.02

11.49-8.42

4.49-5.07

0.66-0.59


ResultsResults• Computer time increases drastically as relative gap is

decreased (more iterations required).• Link fluctuations decreased with increased

convergence.• Large VHT differences from 0% RG value at 0.1% RG.• VHT stabilizes as relative gap is decreased.

ResultsResultsSavings in VHT from Network Improvements

TABLE 8: Difference in VHT from Starting Point AM Crown Scenario (Savings in VHT from Project)VHT Relative Gap (%)

0.10 0.05 0.02 0.01 ~0John Laurie Boulevard Widening 135 138 131 135 134Glenmore Trail Widening 655 646 650 651 655

TABLE 9: Difference in VHT from Starting Point AM Shoulder Scenario (Savings in VHT from Project)VHT Relative Gap (%)

0.10 0.05 0.02 0.01 ~0John Laurie Boulevard Widening 1 0 0 12 11Glenmore Trail Widening 376 380 377 380 379

ResultsResults• Effect of convergence on savings unclear in AM

Crown scenario• Increased convergence lead to increased savings in

AM Shoulder scenario• Important to obtain stable values, particularly in

projects that may not have much benefit in some time periods.

• Most stable VHT results again near 0% RG

ResultsResultsStability of Network

• At 0.1 % RG, Volume differences from link instability begin to outshadow that of the improvement.

• Volumes more refined with increased convergence.

TABLE 10: Maximum Link Volume Differences from Starting Point Scenario Observed, John LaurieBoulevard Widening Project, Truck Penalty of 5 minutes / 100 mScenario Relative Gap (%)

0.10 0.05 0.04 0.03 0.02 0.01 ~0AM Crown 509 493 489 485 480 477 474AM Shoulder 146 138 136 138 138 138 141Numbers in Italics indicate largest change was in an area not associated with the improvement.

Difference in Link Volumes from Volume at 0 Relative Gap

-20

-10

0

10

20

30

40

50

60

70

00.010.020.030.040.050.060.070.080.090.1

Relative Gap (%)

Dif

fere

nce

in

Lin

k V

olu

mes

(V

ehic

les)

McKnight BV W of McCall Way EB

McKnight BV W of McCall Way WB

Sarcee RD N of 44 AV SW NB

Sarcee RD N of 44 AV SW SB

162 AV SW W of Shawinigan Dr SW EB

162 AV SW W of Shawinigan Dr SW WB

Berkshire BV S of Country Hills BV NB

Berkshire BV S of Country Hills BV SB

Deerfoot TR S of Peigan TR SB

Deerfoot TR S of Peigan TR NB

Anderson RD E of 14 ST SW EB

Anderson RD E of 14 ST SW WB

Rundlehorn DR E of 36 ST NE EB

Rundlehorn DR E of 36 ST NE WB

Nose Hill DR N of Crowchild Trail SB

Nose Hill DR N of Crowchild Trail NB

Fairmount DR N of 86 AV SE NB

Fairmount DR N of 86 AV SE SB

5 AV SW E of Centre ST S EB

9 AV SW E of 9 ST SW EB

ResultsResults

ResultsResultsDifference in Link Volumes from Volume at 0 Relative Gap (Excluding Anderson Road)

-15

-10

-5

0

5

10

00.010.020.030.040.050.060.070.080.090.1

Relative Gap (%)

Dif

fere

nce

in L

ink

Vo

lum

es (

Veh

icle

s)

McKnight BV W of McCall Way EB

McKnight BV W of McCall Way WB

Sarcee RD N of 44 AV SW NB

Sarcee RD N of 44 AV SW SB

162 AV SW W of Shawinigan Dr SW EB

162 AV SW W of Shawinigan Dr SW WB

Berkshire BV S of Country Hills BV NB

Berkshire BV S of Country Hills BV SB

Deerfoot TR S of Peigan TR SB

Deerfoot TR S of Peigan TR NB

Rundlehorn DR E of 36 ST NE EB

Rundlehorn DR E of 36 ST NE WB

Nose Hill DR N of Crowchild Trail SB

Nose Hill DR N of Crowchild Trail NB

Fairmount DR N of 86 AV SE NB

Fairmount DR N of 86 AV SE SB

5 AV SW E of Centre ST S EB

9 AV SW E of 9 ST SW EB

ResultsResults• Links approach 0% RG value with increased

assignment.• Anderson Road link has most dramatic change - this is

a link where flip-flopping occurs.• Remaining links are more or less stable around 0.05

% RG (differences are 10 or less)• With Anderson Road included, differences are about

30 or less vehicles at 0.05 % RG

ResultsResults• Assignments below 0.01% RG may stop for a variety

of reasons:– RG or Normalized Gap may go negative and stop

assignment.– Unsure if assignments are then equally converged (same

distance from the optimum objective function)– Differences in assignment should be small, but practitioners

should be aware– EMME/2 will only allow assignment of up to two decimals for

RG -- Must use iterations to get between 0.01 % or 0 % RG.

ConclusionsConclusions• Small differences in large numbers

– Tighter convergence needed to see benefits• Important tradeoffs to be made

– More converged assignment vs. increased computing time

– End criteria depends on use of data and needs

ConclusionsConclusions• For comparing VHT values between scenarios,

RG of 0.01 % recommended• RG of 0.01 % also recommended for link

volumes• If volumes are to be rounded, and practitioners

are aware of areas with link fluctuations, an RG of 0.05 % can be used to save time.

• Knowledge of the importance of convergence will be used in refining mobility benefits process.

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