DYNAMIC NETWORK MICRODYNAMIC NETWORK MICRO …archiv.ivt.ethz.ch/vpl/publications/presentations/v237.pdf · dynamic network microdynamic network micro-assignment withassignment with

DYNAMIC NETWORK MICRODYNAMIC NETWORK MICRO--ASSIGNMENT WITHASSIGNMENT WITHDYNAMIC NETWORK MICRODYNAMIC NETWORK MICRO ASSIGNMENT WITH ASSIGNMENT WITH HETEROGENEOUS USERSHETEROGENEOUS USERS

Hani S. MahmassaniHani S. MahmassaniNorthwestern UniversityNorthwestern UniversityHani S. MahmassaniHani S. MahmassaniNorthwestern UniversityNorthwestern University

ETH- Zurich, October 7 2008

1

INTEGRATING ACTIVITYINTEGRATING ACTIVITY--TRAVEL DECISIONS IN DYNAMIC TRAVEL DECISIONS IN DYNAMIC NETWORK MICRONETWORK MICRO--ASSIGNMENT MODELSASSIGNMENT MODELS

INTEGRATING DEMAND AND SUPPLY


“GIVE ME SUPPLYMODEL THAT IS RICHENOUGH FOR MY DEMAND MODEL”


“GIVE ME DEMANDMODELS THAT ARE

PARSIMONIOUS ENOUGH TO FIT MY PLATFORM”


“GIVE ME SUPPLY “GIVE ME DEMANDMODEL THAT IS RICH MODELS THAT AREENOUGH FOR MY PARSIMONIOUSDEMAND MODEL” ENOUGH TO FIT

MY PLATFORM”


DISINTEGRATING DEMAND AND SUPPLY


THE KEY IS THE PLATFORM:SIMULATION-BASED DTA

CRITICAL LINK 1: LOADING INDIVIDUAL TRIP CHAINS

CRITICAL LINK 2:MODELING AND ASSIGNINGHETEROGENEOUS USERS

Network Simulation-Assignment Modeling g gfor Advanced Traffic System Management

L ti S ifi

CONCEPTUAL FRAMEWORK

“DEMAND”

Location-SpecificTime-Varying

EmissionsDEMAND

ACTIVITY DECISIONS

TRAVEL DECISIONS “EMISSIONS”

Individual and Vehicle Trajectories & Household Activities

j(“modal”) Activities

Trip chains“SUPPLY”

NETWORK MODELING

L ti S ifi

CONCEPTUAL FRAMEWORK“DEMAND” Location-Specific

Time-VaryingEmissionsACTIVITY

DECISIONS-Time and Money

TRAVEL DECISIONS- Virtual vs.

“EMISSIONS”

yExpenditures-Participation and time allocation-Sequencing/Scheduling

physical - Timing- Location- Mode

Individual and Vehicle Trajectories &

duling -....

Household Activitiesj

(“modal”) Activities

“SUPPLY”

Trip chainsNETWORK MODELING-ROUTING-NETWORK LOADING-Vehicle and Flow P tiPropagation-Iterative consistent procedures

Location-SpecificCONCEPTUAL FRAMEWORK

“DEMAND” Time-VaryingEmissionsACTIVITY

DECISIONS-Time and Money


EMISSIONSMODEL



Individual and Vehicle Trajectories & (“modal”) Activities

duling -....

Level of Service

Household Activities ( modal ) Activities

“SUPPLY”

Attributes

Trip chainsNETWORK MODELING-ROUTING-NETWORK LOADING-Vehicle and Flow P tiPropagation-Iterative consistent procedures

Location-SpecificTime Varying

CONCEPTUAL FRAMEWORK“DEMAND” Time-Varying

EmissionsACTIVITY DECISIONS-Time and Money


FIRM LOGISTICSDECISIONS-Production -Sourcing

MOBILE SERVICEPERSONNEL-LocationD ti

EMISSIONSMODEL



Sourcing-Inventory and warehousing -Shipment size and frequency

-Duration-Teaming-Sequencing and Scheduling-…

Individual and Vehicle Trajectories & (“modal”) Activities

duling -....

Level of Service

-Mode

Household Activities ( modal ) Activities

“SUPPLY”

Attributes

Trip chainsNETWORK MODELING-ROUTING-NETWORK LOADING-Vehicle and Flow P tiCommercial vehicle Propagation-Iterative consistent procedures

Commercial vehicleFleet delivery schedules

PO

LILA

YE

INPUTS

DEM

LAND USE

SOCIO

CY

ER

EM

AN

DM

AN

AG

E

SOCIO-ECON-DEMODISTRIBU-

TIONSEM

EN

T

FLEETDISTRI-BUTIONS

PRICING

NETWORK TRAFFICTS NETWORK

STRUCTURETRAFFIC

CONTROLINFORMATION

INP

UT

SUPPLYMANAGEMENT

State of Practice in Network Modeling

1 Most agencies use static assignment models often lacking formal

S a e o ac ce e o ode g

1. Most agencies use static assignment models, often lacking formal equilibration, with very limited behavioral sensitivity to congestion-related phenomena (incl. reliability)

2. Some agencies use traffic microsimulation models downstream from assignment model output, primarily for local impact assessment

3. Time-dependent (dynamic) assignment models beginning to break out of3. Time dependent (dynamic) assignment models beginning to break out of University research into actual application– market still small, fragmented, with many competing claims and absence of standards:

existing static players adding dynamic simulation-based capabilities, INRO (DYNAMEQ) C li (T d) CUBE (V )e.g. INRO (DYNAMEQ); Caliper (Transcad); CUBE (Voyager)

existing traffic microsimulation tools adding assignment (route choice)capability, e.g. AIMSUN-NG; VISSIM/VISUM

standalone simulation-based DTA tools, e.g. DYNASMART-P (distributed by FHWA); VISTA (tie in w. PTV-VISSIM)

State of Practice in Network Modeling (ctd.)

4. Applications to date complementary, not substitutes, for static assignment; primary applications for operational planning purposes: work zones, evacuation,

g ( )

primary applications for operational planning purposes: work zones, evacuation, ITS deployment, HOT lanes, network resilience, etc… Still not introduced in core 4-step process, nor integrated with activity-based models

5 E isting commercial soft are differs idel in capabilities reliabilit and5. Existing commercial software differs widely in capabilities, reliability and features; not well tested.

6. Equilibration for dynamic models not well understood, and often not performedq y p

7. Dominant features, first introduced by DYNASMART-P in mid 90’s:

Micro assignment of travelers; ability to apply disaggregate demand modelsMicro-assignment of travelers; ability to apply disaggregate demand modelsMeso-simulation for traffic flow propagation: move individual entitities, but

according to traffic flow relations among averages (macroscopic speed-density relations): faster execution, easier calibration

Ability to load trip chains (only tool with this capability, essential to integrate with activity-based models)

APPLICATION TO BALTIMORE REGIONAL NETWORK

DTA Model Run25,375 links

11,170 nodes

1,463 TAZs1,463 TAZs

1,901,000 vehicles generated for AM peak period (6-10 AM)

OD Estimation performance on selected linksLink 12893

600

700

800

hr)

Estimation performance for link 12893 (MD 108 at Old Stockbridge Dr/Golden Bell Way)

0

100

200

300

400

500

Volu

me

(veh

/h

Link30 40 50 60 70 80 90

Time (min)

Observed Link Volume (veh/hr) Simulated Link Volume (veh/hr) 15min Simulated Link Volume

Link12893

20000

Cumulative Volume (veh/hr)

12893

8000

10000

12000

14000

16000

18000

20000

0

2000

4000

6000

30 40 50 60 70 80 90

Time (min)

Observed Link Volume (veh/hr) Simulated Link Volume (veh/hr)

OD Estimation performance on selected links (ctd.)Link 6098

700

800

900

Estimation performance for link 6098(Hospital Dr at Oakwood Rd)

0

100

200300

400

500

600

Volu

me

(veh

/hr)

Link0

30 40 50 60 70 80 90

Time (min)


Link 6098Cumulative Volume

(veh/hr)

6098

15000

20000

25000

30000

0

5000

10000

30 40 50 60 70 80 90

Time (min)


OD Estimation performance on selected links

Estimation performance for Link 13326(I-95 NB @ MD Welcome Center North)

Link 13326

7000

8000

2000

3000

4000

5000

6000

7000

Volu

me

(veh

/hr)

Link13326 2000

30 40 50 60 70 80 90

Time (min)


Link 13326Cumulative Volume

(veh/hr)

13326

200000

250000

300000

350000

400000

450000

500000

0

50000

100000

150000

200000

30 40 50 60 70 80 90

Time (min)



THE KEY IS THE PLATFORM:SIMULATION-BASED DTA

CRITICAL LINK 1: LOADING INDIVIDUAL TRIP CHAINS

CRITICAL LINK 2:MODELING AND ASSIGNINGHETEROGENEOUS USERS

A critical missing link: modeling activity/trip chains in network assignment models

Origin

Stop 1

final destination

Dynamic Micro-Assignment of Travel Demand with Activity/Trip Chains

based on work with Ahmed Abdelghany, PhD Dissertation at UT-AustinPhD Dissertation at UT Austin

Capabilities/Operational ModesCapabilities/Operational Modes

Stochastic Temporal-Spatial Micro Assignment of TravelMicro-Assignment of Travel Demand with Activity/Trip Chains

22-- Iterative Iterative simulationsimulationsimulation simulation assignment assignment model (UEmodel (UEmodel (UE model (UE procedure) procedure)

Critical Link 2:

Modeling and assigning h theterogeneous users--

exercising user preferences for path-based attributesp

Essential Aspect of User Response Not Considered in Existing Network Modeling Methods

User HeterogeneityCritical limitation of existing dynamic traffic assignment tools

g g

Each trip-maker chooses a path that minimizes the two major path travel criteria: travel time and out-of-pocket cost (path generalized cost).Conventional traffic assignment models consider a homogeneous perception of tolls by assuming a constant VOT in the path choice model.Empirical studies (e.g. Hensher, 2001; Brownstone and Small 2005; Cirillo et al. 2006) found that the VOT varies significantly across individualsindividuals.

Path A: 45 minutes + $2High

HomeOfficeVOT

L

Path B: 55 minutes + $0

Low VOT

Beyond Value of Time…User Heterogeneity

Present in valuation of key attributes, and riskPresent in valuation of key attributes, and risk attitudes

Value of schedule delay (early vs. late, relative y ( y ,to preferred arrival time), critical in departure time choice decisions.Value of reliability.Risk attitudes.

Causes significant challenge in integrating behavioral models in network simulation/assignment platforms

Dealing with Heterogeneity in Existing Network Models

1 Ignore: route choice main dimension captured; replace travel time by travel1. Ignore: route choice main dimension captured; replace travel time by travel cost in shortest path code, assuming constant VOT.

2. When multiple response classes recognized, discrete classes with specific coefficient values are used; number of classes can increase rapidly; not too common in practice.

3. Some recent developments with DYNASMART-P:3. Some recent developments with DYNASMART P:

Heterogeneous users with continuous coefficient values; made possible by

Breakthrough in parametric approach to bi-criterion shortest pathBreakthrough in parametric approach to bi criterion shortest path calculation.

Include departure time and mode, in addition to route choice, in user responses, in equilibrium frameworkresponses, in equilibrium framework

Recent Methodological Development

Develop Multi-Criterion Simultaneous Route and D t Ti U E ilib i (MSRDUE) d lDeparture Time User Equilibrium (MSRDUE) models and algorithms

Address the heterogeneous user preference of path and/or dd ess t e ete oge eous use p e e e ce o pat a d/odeparture time choices in response to time-varying toll charges. Capture traffic flow dynamics and spatial and temporal vehicular interactions (simulation based approach)interactions (simulation-based approach). Adhere to the time-dependent generalization of Wardrop’s UE principle (gap function measures the deviation from equilibrium).Be deployable on road traffic networks of practical sizes (vehicle-based implementation technique).

Problem Statement

Assumptions:G(N, A), discretized planning horizon, and time-dependent link tolls.Define schedule delay as the difference between actual and preferred arrival times (PAT).

Every trip-maker has his/her own PAT interval θEarly schedule delay (ESD) and late schedule delay (LSD)Value of ESD (VOESD β) and value of LSD (VOLSD λ)

Th i d t i t i d b t i k ith θ βThe experienced trip cost perceived by a trip-maker with θ, α, β,and λ

)()(),,,( θλθβαλβαθ τττττodpodpodpodpodp LSDESDTTTCG ×+×+×+=

where

VOT α, VOESD β, and VOLSD λ are continuously distributed

ppppp

},0max{)( midlbodpESD τθθτ −= },0max{)( ubmid

odpLSD θτθτ −=Path generalized cost Schedule delay cost

, β, yacross trip-makers with given probability density functions and feasible ranges.

Problem Statement (ctd.)

Departure time and path choice behavioral assumption: Each trip maker chooses the alternative that minimizes the experiencedEach trip-maker chooses the alternative that minimizes the experienced trip cost with respect to his/her PAT, VOT, VOESD, and VOLSD.An alternative is a combination of arrival time interval and the corresponding least generalized cost path (that arrives the destination at that arrival time interval).

Multi-criterion simultaneous route and departure time UE (MSRDUE)For each OD pair, cannot decrease the experienced trip cost (given user’s particular VOT, VOESD, VOLSD, and PAT interval) by unilaterally changing departure time and/or path.

Each trip-maker is assigned to the alternative that has the least trip cost with respect to his/her own PAT VOT VOESD and VOLSDcost with respect to his/her own PAT, VOT, VOESD, and VOLSD.

MSRDUE problem: Under a given time-dependent road pricing scenario, solve for the

departure time and path flow patterns satisfying the MSRDUE conditions.

Why is this problem difficult?y pRelaxation of VOT from constant to continuous random variable

Find an equilibrium state resulting from the interactions of (possibly infinite) many classes of trips, each of which corresponds to a class-specific VOT.

Comp ting and storing s ch a grand path set is comp tationallComputing and storing such a grand path set is computationally intractable and memory intensive in (road) network applications of practical sizes

Parametric Analysis Method (PAM) to find the set of extreme y ( )efficient (or non-dominated) path trees

In the disutility minimization-based path choice modeling framework with convex disutility functions

CostDominated paths

with convex disutility functionsAll trips would choose only among the set of extreme efficient pathsApplications in static assignment

Non-extreme efficient paths

(Dial, 1996; Marcotte, 1997)

Time

Extreme efficient paths

(Henig, 1985)

Determine VOT, VOESD, and VOLSD breakpoints that define multi-

Sequential Parametric Analysis Method (SPAM)

user classes, and find the least trip cost (extreme non-dominated)alternative for each user class

Repeat the two stages for each destination: d = 1 D

1

Stage 1: parametric analysisf O

d D

Repeat the two stages for each destination: d = 1,...,D..... .....

of VOT

minα maxα1α 2α 3α

Tr(1) Tr(2) Tr(3)St 2parametric analysis

of VOESDparametric analysis

of VOLSDminβ minλ maxλ

Stage 2:

1β2β 1λ2λmaxβ1β2β 1λ2λ

Repeat the second stage for each VOT subinterval: b=1,...,3

P t i A l i f VOT t 1 f th SPAM

Determine the breakpoints that partition the feasible VOT range and define the

Parametric Analysis of VOT – stage 1 of the SPAM

Determine the breakpoints that partition the feasible VOT range and define the master user classes, and find time-dependent least generalized cost path tree for each user class.

VOT

αmin αmax

Tree(1) Tree(2) Tree(3) Tree(4) Tree(5) Tree(6)

Time •Each tree consists of time-dependent least generalized cost paths from all origin nodes to a d i i d f ll i ldestination node, for all arrival time intervals.•To determine the subinterval of VOT, in which the current tree

Cost

VO , w c t e cu e t t eeTr(α) is optimal.

Parametric Analysis of VOESD and VOLSD for a VOT subinterval – stage 2 of the SPAM

Given a time-dependent extreme efficient path tree Tr(b)di t th VOT bi t l [ b 1 b) th t icorresponding to the VOT subinterval [α b-1, α b), the parametric

analyses of VOESD and VOLSD are conducted in an expanded network.

Arrival Times PAT intervals

),( 1τd

)( τd

p1

))(,( 11 τδτ oo −

))(,( 22 τδτ oo −

),'( 1θdESD/LSD

),( 3τd

),( 2τdp2

p3

))(,( 33 τδτ oo −

),'( 2θd

),'( 3θd

),( 4τd

p3

p4

))(,( 44 τδτ oo −),'( 4θd

p5

))(,( 55 τδτ oo − ),( 5τd),'( 5θd

Parametric Analysis of VOESD and VOLSD for a VOT subinterval

A lAn example

1τArrival Times

1θPAT

))(,( 11 τδτ oo − ESD+

minβ

2τ 2θ))(,( 22 τδτ oo −

+p1

p2λ

3τ

4τ

3θ

4θ

))(,( 33 τδτ oo −

))(( τδτo

currentPATp3

1β

maxβ 1λ

maxλ

4 4))(,( 44 τδτ oo −

5τ))(,( 55 τδτ oo − 5θLSD

+

p4

maxβ

+p5

minλ

Parametric Analysis of VOESD and VOLSD

Output of the SPAM

yfor a VOT subinterval

Output of the SPAMVOESD breakpoints that define the subintervals, and the least trip cost alternative for each subinterval. ∀b, ∀θ,

}|{)( min),(10max),(10 βββββββββθβ θθ =>>>>>== bMmbMb

VOLSD breakpoints that define the subintervals, and the least trip cost alternative for each subinterval. ∀b, ∀θ,

}......|,...,,{),( βββββββββθβ >>>>>b

),(,...,1 ,*)*,( ,),[ ,,,1 θτββ θθ bMmp mbb

mm =−

Multiple user classes: for each VOT subinterval b and PAT θ,

}......|,...,,{),( min),(10max),(10 λλλλλλλλλθλ θθ =>>>>>== bNnbNb),(,...,1 ,*)*,( ,),[ ,,,

1 θτλλ θθ bNnp nbbnn =−

Multiple user classes: for each VOT subinterval b and PAT θ,

Simplified as u(b,θ, m, n)The corresponding set of least trip cost alternatives

),(,...,1 ),,(,...,1 ),,,,( ),(),( θθθ θλθβ bNnbMmnmbu bb ==

The corresponding set of least trip cost alternatives

),,(),,(),,,( ,, θθ θθθ bodbodod nbaltmbaltnmbalt ∪=

Column Generation-based MSRDUE algorithm

InputOD demand link tollsOD demand, link tolls,VOT distribution, andinitial path assignment

InitializationSequential Parametric

Analysis Method (SPAM)InitializationTraffic simulation toevaluate initial path

assignment

Analysis Method (SPAM)VOT, VOESD, VOLSD

breakpoints definig multi-userclasses and extreme efficient

alternatives for each class

ConvergenceChecking?

Output path flowsand terminateYES

NO

Multi-class PathFlow Updating

Scheme

Outer Loop:Multi-class Dynamic

Network LoadingTraffic Simulation

Outer Loop:Alternative Generation Inner Loop:

Equilibration

ConvergenceChecking?

YES NO

Multi-Class Flow Updating and Convergence Checking

Multi-Class Alternative Flow Updating SchemeMultiple user classes u(b θ m n) are naturally determined by the

Co e ge ce C ec g

Multiple user classes u(b,θ, m, n) are naturally determined by the SPAM.Decomposes the problem into many (b,θ,m,n,o,d) sub-problems and solves each of them by adjusting OD flows between non-least y j gtrip cost alternatives and the least trip cost alternative.Extension of the multi-class path flow updating scheme for the BDUE

Convergence CheckingGap

∑ ∑∑ ∑ Δ×= ,, ),,,(),,,()( lodp

lodp

l nmbnmbrrGap ττ θθ

Average Gap∈),,,( ),,,(),(nmbu o d nmbaltp odθ θτ

∑ ∑∑ ∑∈

Δ×)( )()(

,, ),,,(),,,()( nmbu o d nmbaltp

lodp

lodp nmbnmbr

θ θτ

ττ θθ

∑ ∑∑ ∑∈

∈=

),,,( ),,,(),(

,),,,( ),,,(),(

),,,()(

nmbu o d nmbaltp

lodp

nmbu o d nmbaltp

od

od

nmbrrAGap

θ θτ

τθ θτ

θ

Numerical Experiments and Results

Purpose


Examine the algorithmic convergence property and solution quality of the algorithm Investigate how the random parameters would affect departure time and path flow patterns (or toll road usage) under different dynamic pricingpath flow patterns (or toll road usage) under different dynamic pricing scenarios (i.e. to compare the random and constant parameter models).

Random parametersVOT di t ib ti N($0 4/ i $0 2/ i ) [ min max] [0 01 3 0]VOT distribution: N($0.4/min, $0.2/min), [α min,α max] = [0.01, 3.0]

(Lam and Small, 2001; Brownstone and Small, 2005; Southern CA)VOESD distribution: N($0.3/min, $0.15/min), [β min, β max] = [0.01, 2.0]VOLSD di t ib ti N($1 8/ i $0 6/ i ) [λ min λ ma ] [0 25 4 0]VOLSD distribution: N($1.8/min, $0.6/min), [λ min, λ max] = [0.25, 4.0]

(economic judgments based on the results reported in Small (1982))

Arrival time and PAT intervals: 5 minutes.


E i t d t d th F t W th t k (TX)


Experiment conducted on the Fort Worth network (TX)Select a critical OD pair that accounts for 25% of total demand.

1200O

400

600

800

1000um

ber o

f Veh

icle

s

PAT pattern

0

200

0-5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

Nu

Pricing Scenario

0-20 minutes

20-40 minutes

40-60 minutes

60-80 minutes

80-100 minutes

100-120 minutes

120-150 minutes

#1 (low) $0.05 $0.20 $0.35 $0.50 $0.35 $0.20 $0.05 #2 (mid) $0.25 $0.40 $0.55 $0.70 $0.55 $0.40 $0.25 #3 (high) $0.45 $0.60 $0.75 $0.90 $0.75 $0.60 $0.45

D

dynamic pricing scenarios


Experiment conducted on the Fort Worth network (TX)Con ergence pattern and sol tion q alit in terms of A erageConvergence pattern and solution quality in terms of Average Gap.Convergence pattern in terms of departure time distribution

0 800

1.000

1.200Random Parameters

Constant Parameters

1200

1400

1600

cles

Initial Sol.

Iteration 1Iteration 5

0 200

0.400

0.600

0.800

Aga

p (m

in)

200

400

600

800

1000

Num

ber o

f Veh

ic Iteration 5

Iteration 10

0.000

0.200

1 2 3 4 5 6 7 8 9 10

Iteration

0

200

0-5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

departure time distribution(random parameter model)

average gap


E i t d t d F t W th t k (TX)


Experiment conducted on Fort Worth network (TX)Convergence pattern in terms of the number of schedule delay vehicles (i.e. early, late, and on-time vehicles) in the random parameter model

4000

4500

5000

1500

2000

2500

3000

3500

Num

ber o

f Veh

icle

s

# of ESD

# of LSD

# of OnTime

0

500

1000

0 1 2 3 4 5 6 7 8 9 10

Iteration

N




Experiment conducted on the Fort Worth network (TX)Compare the differences in departure time distribution and toll road usage between random and constant parameter models

800

1000

1200

cles

Random Parameter ModelConstant Parameter Model

500

600

cles

Random Parameter ModelConstant Parameter Model

200

400

600

800

Num

ber o

f Veh

ic

100

200

300

400

Num

ber o

f Veh

ic

0

0-5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

00-

5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

departure time distribution Time-varying toll road usage




Experiment conducted on the Fort Worth network (TX)Comparison of departure time distribution and toll road usage under different dynamic pricing scenarios

800

1000

1200

hicl

es

Low Price

Mid PriceHigh Price 500

600

700

hicl

es

Low Price

Mid PriceHigh Price

200

400

600

Num

ber o

f Veh

100

200

300

400

Num

ber o

f Veh

0

0-5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

00-

5

10-1

5

20-2

5

30-3

5

40-4

5

50-5

5

60-6

5

70-7

5

80-8

5

90-9

5

100-

105

110-

115

Time (min)

departure time distribution Time-varying toll road usage

Concluding RemarksConcluding Remarks

Integration of activity-based models and network models requires:disaggregate micro-assignment platform; simulating traffic dynamics at mesodisaggregate micro-assignment platform; simulating traffic dynamics at mesoscale allows application to large networks Retaining activity/trip chains as basic assignment entity; do not break into individual tripsCapturing user heterogeneity while retaining computational tractabilityCapturing user heterogeneity while retaining computational tractabilityIntegration is more than mere “juxtaposition” or back and forth iteration between models designed for separate purposes

DTA software can readily integrate today with rich activity-basedDTA software can readily integrate today with rich activity based micro-level software through “vehicle” and “path” filesEquilibration with choice dimensions other than route choice, with general VOT distribution still in experimental software stageRapid development in new algorithms and intelligent implementations of equilibration algorithms designed to operate with particle-based micro-assignment modelsE i t d t d fi d ilib i ( ifi dExperience to date: procedures can find equilibrium (verified through gap function methods), but uniqueness not likely for the general case with heterogeneous users (known from static case)

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DYNAMIC NETWORK MICRODYNAMIC NETWORK MICRO …archiv.ivt.ethz.ch/vpl/publications/presentations/v237.pdf · dynamic network microdynamic network micro-assignment withassignment with