does dta work in practice?

DOES DTA WORK IN PRACTICE?

FIRMING THE FOUNDATIONS, PUSHING THE BOUNDARIES

Hani S. Mahmassani Northwestern University

DTA 2016, Sydney, NSW, Australia, June 28 2016

KEY TAKEAWAYS §  DTA has come a long way since the seminal work by Merchant and Nemhauser in 1978, both as a core topic in transportaIon science, as well as an essenIal component of the modern toolkit of transportaIon modelers for planning and operaIons applicaIons. §  Deeper insight into the various models’ properIes has been gained, and robust algorithms have emerged to compute equilibria and other fixed points of the models. §  At the same Ime, the boundaries of applicaIon have conInued to evolve through §  computaIon over larger-‐scale networks, §  integraIon with acIvity-‐based models (on the planning side), §  consideraIon of heterogeneous user preferences in applicaIons to wider range of policy quesIons and intervenIons (e.g. managed lanes, value pricing), and §  providing a core capability for real-‐Ime esImaIon and predicIon (for online operaIons).

§  Increasingly it is the tool of choice for analyzing impacts of new technologies, new service concepts, novel policies because DTA tools capture four criIcal phenomena: (1) Behavior, (2) Networks, (3) Conges8on, and (4) Dynamics. §  Yet agency pracIIoners are not totally on board §  Growing range of moIvaIng applicaIons raises many challenges– both fundamental and methodological, as well as pracIcal and implementaIon-‐related (devil is in the details). §  Successful applicaIon requires solid theory, and powerful methodological foundaIonal research moIvated by these challenges. 1/14/2013

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Does DTA work in pracIce? §  StaIc assignment models are much more “forgiving” than dynamic assignment methods §  §  §  § 

Allow incomplete networks Do not require juncIon representaIon: more complex dynamics at nodes than on links. V/C > 1 does not bother anybody No flow breakdown, no gridlock…

§  Demand models used in pracIce developed for an era of staIc network models, even though they purport to capture detailed micro-‐dynamics. §  Inefficient representaIons and data structures from supply standpoint §  Uninformed by network computaIons §  Ohen produce temporal and spaIal inconsistencies that are not “caught” by trip-‐based assignment

§  Many (most) integraIon efforts in pracIce have not ajempted “deep integraIon”, but instead have struggled through different levels of interfacing.

§  For agencies, DTA has not replaced staIc models, but is used for special studies (corridor management, work zones, evacuaIon), more as a simulaIon tool with route diversion than as primary network modeling tool. 1/14/2013

NEXT

3

WHAT AGENCIES AND THEIR CONSULTANTS DO DEMAND

SUPPLY

INTEGRATE

?

CONVERT

CONVERT

CONVERT

INTERFACE

4

WHAT VENDORS DO DEMAND

SUPPLY

INTEGRATE

?

JUXTAPOSE 5

WHAT WE (DTA’ers) DO DEMAND

SUPPLY

INTEGRATE? 6

DIS INTEGRATING DEMAND AND SUPPLY

THE KEY IS THE PLATFORM: SIMULATION-BASED DTA

return

CRITICAL LINK 1: LOADING INDIVIDUAL ACTIVITY CHAINS CRITICAL LINK 2: MODELING AND ASSIGNING HETEROGENEOUS USERS CRITICAL LINK 3: MulB-‐scale modeling: consistency between temporal scales for different processes

The Context:

Evolu9on Towards Behavioral Realism in Modeling and Forecas9ng Tools

AcIvity-‐scheduling, real-‐Ime response to informaIon AcIvity-‐based models Trip chains Disaggregate, choice models

Behavioral Realism Prospect theory, CumulaIve PT Learning dynamics Bounded raIonality, thresholds, heurisIcs, ComputaIonal process models Aptudes, percepIons Random uIlity Consumer theory

4-‐step SequenIal StaIc

Dynamics

Behavioral Realism Learning dynamics

Within-‐ Day-‐to-‐ 4-‐step day day SequenIal StaIc

Long-‐term EvoluIon & AdaptaIon Dynamics

Dynamic Equilibrium Convergence?

Disequilibrium? Stability? EvoluIonary paths

AdapIve strategies

Behavioral Realism

4-‐step SequenIal StaIc Travel decisions

Freight, logisIcs AcIvity and Ime use decisions Energy, NETWORK Environment ResidenIal and land use TelecommunicaIon, telemobility

IntegraIon

FLOW PROCESSES

Dynamics

AcIvity-‐scheduling, real-‐Ime response to informaIon AcIvity-‐based models

Behavioral Realism Learning dynamics

Trip chains Disaggregate, choice models Within-‐ Day-‐to-‐ Long-‐term 4-‐step day day EvoluIon & SequenIal AdaptaIon StaIc Freight, Dynamics Travel decisions logisIcs Dynamic AcIvity and Ime use decisions Equilibrium Convergence? Energy, Environment ResidenIal and land use Disequilibrium? Stability? EvoluIonary paths TelecommunicaIon, telemobility AdapIve strategies

IntegraIon

Network Flow Processes: What Planning Models Missed

LINK PERFORMANCE FUNCTIONS (volume-‐delay curves)

Travel Ime

•  RepresentaIon of traffic flow processes on roadway faciliIes (incl. juncIons) •  Bone of contenIon between economists and traffic scienIsts •  Limited appreciaIon in both camps of interpretaIon flow

Backward-‐bending curve

Travel Ime

Average Speed

Traffic Science (fundamental diagram)

flow

flow

Travel Time Index

25 20 15

congested

10

uncongested

5 0 0

500

1000 1500 2000 Flow rate (vphpl)

2500

Behavioral Realism

Process models of cogniIon and learning in Integrated networks acIvity-‐based demand & network microsimulaIon

4-‐step SequenIal StaIc

IntegraIon

Dynamics

State of advanced practice: Microsimulation of traveler choices on multimodal networks with explicit simulation of flow processes (simulation-based multimodal DTA)

Important role played by FHWA and SHRP2 program in development and initial demonstration.

Integrated acIvity-‐based demand & network microsimulaIon

MAJOR INTEGRATION CHALLENGE: AddiIonal behavioral realism on the demand/acIvity side translates into major challenges for path finding and computaIonal burden in network modeling side. Examples: 1.  Heterogeneous users– different values of Ime for different users, thus possibly different shortest paths; approach: parametric shortest path for conInuously distributed VOT (in pricing applicaIons). 2.  Travel Ime reliability as ajribute in choice models (of route, mode, departure Ime…): non-‐addiIve across links to obtain path disuIliIes or generalized costs. 3.  Nonlinear uIlity funcIon specificaIons– non-‐addiIvity. 4.  Different behavioral rules (other than disuIlity minimizaIon), especially for decisions under risk– path finding in stochasIc dynamic networks.

My Big Themes for DTA ApplicaIons q  Heterogeneity

§  Supply-‐side (flow enIIes) §  Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

q  MulBmodality

§  Varying forms of urban/regional transit §  TNC’s (shared mobility, ride-‐hailing, hybrid transit) §  Service vehicles (freight, deliveries, snow plows…)

q  StochasBcity

§  Travel Ime reliability impact on user choices (VOR in generalized cost, alt. rules) §  UIlity dispersion and stochasIc dynamic equilibria (path correlaIons)

q  IntegraBon with acBvity-‐based models q  SpaBal learning and day-‐to-‐day dynamics §  Role of informaIon, social influence

q  Online DTA-‐based esBmaBon, predicBon and control

§  PredicIve control framework, off-‐line evaluaIon of online DTA-‐based predicIve control

q  Leveraging (vehicle, traveler) trajectories for calibraIon and validaIon of network models 1/14/2013

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My Big Themes for DTA ApplicaIons q Heterogeneity §  Supply-‐side (flow enIIes) City streets increasingly directed to mulIple users Not limited to developing countries or Amsterdam Limited observaIon for performance model development

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q Heterogeneity

§ Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

Heterogeneous Users with Different Value of Time For Chicago regional network: Four Different Continuous Value of Time Distributions for different groups of users based on income level (Vovsha et al., 2013)

Household income group

N HH

Mean Person in HH

N Person

HH weights

Person weights

0-30,000 [$]

1,081,423

1.99

2,153,288

0.274

0.202

30,0001-60,000 [$]

1,189,229

2.65

3,156,618

0.302

0.296

60,001-100,000 [$]

988,625

3.15

3,119,355

0.251

0.292

100,001+ [$]

684,051

3.29

2,248,882

0.173

0.211

Total

3,943,328

2.77

10,678,143

1

1

0-30K

30-60K

60-100K

100K+

Aggregated

VOT

6.01

8.81

10.44

12.86

9.68

VOTTollConst

2.18

3.20

3.79

4.67

3.48

VOTTSD

0.80

1.17

1.39

1.71

1.27

VOTTSD w/o network ratio

1.52

2.22

2.64

3.25

2.42

q Heterogeneity

§ Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

τ τ c'τodp (α ) = TC odp + α × TTodp

Determine the breakpoints that parIIon the feasible VOT range and define the master user classes, and find Ime-‐dependent least generalized cost path tree for each user class. Tree(1)

Tree(2)

Tree(3)

Tree(4)

Tree(5)

αmin Time

Tree(6)

VOT

αmax • Each tree consists of Ime-‐ dependent least generalized cost paths from all origin nodes to a desInaIon node, for all arrival Ime intervals. • To determine the subinterval of VOT, in which the current tree Tr(α) is opImal. Cost

Mahmassani et al. (2006), & Lu, & Mahmassani, (2008).

My Big Themes for DTA ApplicaIons q  Heterogeneity §  Supply-‐side (flow enIIes) §  Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

q  MulBmodality §  Varying forms of urban/regional transit §  TNC’s (shared mobility, ride-‐hailing, hybrid transit) §  Service vehicles (freight, deliveries, snow plows…)

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Least Cost Hyperpaths in MulI-‐Modal Transit Networks ProperIes • 

MulI-‐modal –  –  –  – 

• 

Transit modes Walking Biking Structurally easy to add new modes including passenger cars and other highway modes

MulI-‐pajern (route variaIons)

–  A transit route may consist of more than one sequence of stops/staIons

• 

Movement/approach dependent

–  The cost at a node, as well as the ajracIve set of opIons is dependent on what link, mode and pajern one arrives at that node

• 

Time-‐dependent

• 

Frequency-‐based

• 

Vehicle capacity constrained

Stay

Get off and walk Get off and wait for red bus Keep walking Wait for a bus Stay Get off and walk Get off and wait for blue bus

23

Least Cost Hyperpaths in MulI-‐Modal Transit Networks Hyperpath

•  Assume a transit traveler can walk either to

–  To Stop A, where there is a train service going to his desInaIon –  Or to Stop B, where there are three slower bus services all going to his desInaIon

•  In a shortest path formulaIon, he would always go to Stop A and wait for the train. •  Assuming that the headway distribuIons of the three buses are independent of each other, the combined waiIng Ime at Stop B would be 5 min. with a boarding probability of 1/3 for each bus. •  A hyperpath is a strategic path where the choice of opIons are not binary but probabilisIc. A

B

15 min. wait, 40 min. travel: 2x15 + 40 = 70

5 min. wait, 50 min. travel: 2x5 + 50 = 60 24

Least Cost Hyperpaths in Mul3-‐Modal Transit Networks MulI-‐Modal and Time-‐Dependent Cost Structure at a node

25

Transit Assignment Time-‐Dependent User Equilibrium

26

Transit Assignment & Simula3on Transit SimulaIon: NUTrans

Least Cost Hyperpaths

Experience

Assignment

27

Transit Simula3on SimulaIon of Travelers

•  Moving travelers in the network using Ime queues for every instance •  •  •  • 

Walking Biking WaiIng Boarding or being rejected

•  Capturing

•  The heterogeneity in the experienced waiIng •  The disconInuity in transfers/missed connecIons •  The disconInuity in boarding/gepng rejected 28

Transit Simula3on SimulaIon of Vehicles

•  Moving vehicles in the network using Ime queues for every instance •  Vehicle movement •  Riders on board •  AlighIng travelers •  Seat assignment

•  Capturing •  The disconInuity in seaIng/standing

29

Transit Assignment & Simula3on Test Network

CTA Bus and Rail Network •  1,072 zones •  13,754 nodes

•  11,610 stops/staIons •  2,144 centroids

•  63,602 links •  134 routes •  823 pajerns •  Vehicle trips

•  20,736 for full day •  5,975 for 7 am – 12 pm

•  Transit traveler demand

•  1,261,320 for full day •  438,687 for 7 am – 12 pm 30

Transit Assignment & Simula3on Results – Full Day

31

Transit Assignment & Simula3on Results – Full Day

32

My Big Themes for DTA Applica3ons q Heterogeneity §  Supply-‐side (flow enIIes) §  Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

q MulBmodality §  Varying forms of urban/regional transit §  TNC’s (shared mobility, ride-‐hailing, hybrid transit) §  Service vehicles (freight, deliveries, snow plows…) Fundamental Ques9ons: What is nature of equilibrium in this market? Demand paIern and operator/TNC company’s behavior?

1/14/2013

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My Big Themes for DTA Applica3ons q Heterogeneity §  Supply-‐side (flow enIIes) §  Demand-‐side (user preferences, e.g. VOT and VOR; behavior rules– BRUE)

q MulBmodality §  Varying forms of urban/regional transit §  TNC’s (shared mobility, ride-‐hailing, hybrid transit) §  Service vehicles (freight, deliveries, snow plows…) Required capabili9es: 1. Modeling and simula9ng tours in DTA 2. Decisions result of company ac9on– op9mizing logis9cs opera9ons 3. Incorpoa9ng real-‐9me informa9on in fleet opera9ons. 4. Ques9on: Is Equilibrium appropriate for these vehicles? Approach is to provide best equilibrated travel 9mes for op9mal rou9ng calcula9ons. 1/14/2013

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A Priori Rou3ng Planner: Leveraging DTA Model & Simulator § Time-‐dependent travel Imes are given by DTA model and simulator based on equilibrated network. § A priori rouIng planner adopts soluIon algorithm for TDVRPTW (Time-‐Dependent Vehicle Rou9ng Problem with Time Window) with Ime-‐dependent travel Imes. § SoluIons are then re-‐simulated in DTA simulator under various traffic events, recognizing all waiBng Bmes and service Bmes at customer sites. § SIMILAR CAPABILITY ENVISIONED FOR AUTONOMOUS VEHICLE MODELING (Jiang & Mahmassani, 2013) 35

My Big Themes for DTA Applica3ons q Heterogeneity


q MulBmodality


q StochasBcity


q IntegraBon with acBvity-‐based models q SpaBal learning and day-‐to-‐day dynamics §  Role of informaIon, social influence

q Online DTA-‐based esBmaBon, predicBon and control


q Leveraging (vehicle, traveler) trajectories for calibraIon and validaIon of network models

1/14/2013

36

IntegraIon of DTA with ABM –  Based on recently completed work on development of integrated mulImodal DTA-‐ABM capability for the Chicago Metropolitan Agency for Planning –  Acknowledgment: •  Peter Vovsha, PB Americas Inc. •  Kermit Wies, CMAP

Research ObjecIves Ø Create an integrated micro-‐level mulImodal network analysis and predicIon capability– building on a micro-‐ simulaIon acIvity-‐based model (ABM) within a dynamic mulImodal network simulaIon-‐assignment capability. Ø MulImodal in the core– transit and non-‐auto travel essenIal, not aherthought. Ø Explore and implement appropriate equilibraIon concept and algorithmic scheme for the integrated framework. Ø Large-‐scale network applicaIon: computaIonal implicaIons Ø A robust producIon tool for CMAP planning work

EQUILIBRIUM CONCEPT FOR ABM AND DTA INTEGRATION

39

WHAT INTEGRATION IS NOT Aggregate LOS OD Skims Feedback Microsimulation ABM

Aggregate LOS skims for all possible trips

List of individual trips

Microsimulation DTA

ALL ABOUT THE CHAIN!

1/14/2013

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DefiniIon of Equilibrated State Ø Individual travelers cannot increase their uIlity by unilaterally changing their ac8vity chain (acIviIes, duraIons, schedule). Ø An ac8vity chain is defined by a sequence of acIviIes with departure Ime and duraIon for each of acIvity in the chain.

42

DefiniIon of Variables Ø ABM outputs individual trip chain with acIvity chain, departure Ime, and acIvity duraIons: ai = [ai1 , ai2 , … , aiM ] τ iABM = [τ i1, ABM ,τ i2, ABM ,…,τ iM , ABM ] d i = [d i1 , d i2 , … , d iM ] Ø DTA load individual trip chain and outputs experienced travel Ime and/or generalized travel cost: a = [ai1 , ai2 , … , aiM ]

i DTA

τ i = [τ i1, DTA ,τ i2, DTA ,…,τ iM , DTA ] d i = [d i1 , d i2 , … , d iM ] 43

Fixed Point FormulaIon U(a,τ , d ) = S(P(A(U(a,τ,d))))

Experienced UBlity or Generalized Cost

44


Experienced UBlity or Generalized Cost

45


Experienced UBlity or Generalized Cost AcBvity Chain from ABM

46


Experienced UBlity or Generalized Cost AcBvity Chain from ABM User path (trajectory) from assigning acBvity schedules

47


Experienced UBlity or Generalized Cost AcBvity Chain from ABM User path (trajectory) from assigning acBvity schedules UBlity obtained from simulaBng user path (trajectory) 48


Experienced UBlity or Generalized Cost AcBvity Chain from ABM User path (trajectory) from assigning acBvity schedules UBlity obtained from simulaBng user path (trajectory) 49

ProperIes

Fixed Point Equilibrium FormulaIon

•  SoluIon Existence o ConInuity of the FuncIons

•  SoluIon Uniqueness o Monotonocity of the FuncIons

•  SoluIon Stability

50

Challenges

Fixed Point Equilibrium

TheoreIcal Challenges •  Large scale problems •  No closed form funcIon •  Unavailable derivaIves PracIcal Challenges •  Large scale Networks –  Consistency of spaIal and temporal resoluIons between ABM and DTA –  Maintaining spaIal and temporal consistencies of interdependent trips within DTA 51

Linking the Variables ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ ⎝ d i ⎠

MulB-‐Modal DTA

U iABM Planned Individual UBlity

TT GC

⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ ⎝ d i ⎠

U iDTA Experienced Individual UBlity 52

Convergence Criteria: Gap Measure I

ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

MulB-‐Modal DTA

U iABM Planned Individual UBlity

⎛ ai* ⎞ ⎜ ⎟ ⎜τ i* ⎟ ⎜ * ⎟ ⎜ d i ⎟ ⎝ ⎠

U i*

OpBmal Individual UBlity

TT GC

⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

U iDTA Experienced Individual UBlity 53

Convergence Criteria: Gap Measure II

ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ ⎝ d i ⎠

MulB-‐Modal DTA

U iABM ,k

TT GC

⎛ ai*,k ⎞ ⎜ ⎟ ⎜τ i*,k ⎟ U i*,k ⎜ ⎟ * ⎜ d i ,k ⎟ ⎝ ⎠ ⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ ⎝ d i ⎠

U iDTA ,k

* At equilibrated state, we have: U iDTA = U ,k i ,k (ak ,τ k , d k ), ∀i ∈ N

1 GAP = N

N

DTA * ( U − U ∑ i , k i , k ( ak , τ k , d k ) ) i

54

SoluIon Approach: Outer Loop ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

U iABM ,k

DTA

TT GC

⎛ ai*,k ⎞ ⎜ ⎟ * ⎜τ i ,k ⎟ U i*,k ⎜ ⎟ ⎜ d i*,k ⎟ ⎝ ⎠ ⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

U iDTA ,k

The planned acBvity chain for the next iteraBon is updated for a subset of travelers based on the magnitude of their gap measure (e.g. likelihood of selecBon for update proporBonal to experienced gap). * $ ! ai,k+1 $ ! ai,k $ ! ai,k # & # & # & ABM ABM * DTA * #τ i,k+1 & = #τ i,k & + f (Ui,k ,Ui,k ) #τ i,k & ## && ## && ## * && " di,k+1 % " di,k % " di,k %

55

SoluIon Approach: inner loop ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

MulB-‐Modal DTA ⎛ ai ⎞ ⎜ Adj ⎟ ⎜τ i ⎟ ⎜ Adj ⎟ ⎝ d i ⎠

⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

TT GC

Schedule Adjustment

ObjecBve: schedule consistency

56

Schedule Consistency: Planned AcIvity Chain

57

Schedule Consistency: Experienced AcIvity Chain

58

Schedule Consistency: Experienced AcIvity Chain

The experienced arrival Bme is later than the planned depart Bme

59

Schedule Consistency: Adjusted AcIvity Plan

60

Schedule Consistency: Adjusted AcIvity Plan

Adjust the depart Bme and duraBon Bme of the previous acBvity

61

SoluIon Approach: ComputaIonal ConsideraIons for Outer Loop

ABM ⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

U iABM ,k

DTA

TT GC

⎛ ai*,k ⎞ ⎜ ⎟ ⎜τ i*,k ⎟ U i*,k ⎜ ⎟ * ⎜ d i ,k ⎟ ⎝ ⎠ ⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

U iDTA ,k

However calculaIng UDTA and U* requires full run of ABM which is computaIonally demanding; instead we propose defining “surrogate uIliIes” that do not require ~ DTA ~ * 62 running the full ABM U and U

SoluIon Approach: ComputaIonal ConsideraIon for Outer Loop Run ABM for selected users ⎛ ai*,k ⎞ ⎜ ⎟ ⎜τ i*,k ⎟ ⎜ ⎟ * ⎜ d i ,k ⎟ ⎝ ⎠

⎛ ai ⎞ ⎜ ABM ⎟ ⎜τ i ⎟ ⎜ ⎟ ⎝ d i ⎠

U

ABM i ,k

MulB-‐Modal DTA

TT GC

⎛ ai ⎞ ⎜ DTA ⎟ ⎜τ i ⎟ ⎜ ⎟ d ⎝ i ⎠

~ *

U i ,k

~ DTA

U i ,k

63

Methodology

ABM DTA IntegraIon

•  Surrogate Gap Measure: ABM Planned AcIvity DuraIon Planned Trip Arrival Time Planned Trip Departure Time

Surrogate Gap UDTA , U*

ABM U

GC DTA

64

Problem Approach

Level 2 IntegraIon

Defined Gap Measures •  Inconsistent Schedule Penalty •  Number of NegaIve AcIvity Households •  DTA relaIve gap

65

Problem Approach

Level 2 IntegraIon

SelecIon Strategies •  Schedule Adjustment o Only Households with unrealisIc schedules o Random selecIon + unrealisIc schedule households o Households with higher penalIes than a pre-‐specified threshold

Problem FormulaIon 𝑃𝐿𝐷 𝑖 : ( 𝐹𝑃𝐿𝐷 𝑖 , 𝑃∗ 𝐿𝐷 𝑖 , 𝑃𝐿𝐷 𝑖 )

AcIvity Scheduling Penalty associated with late departure of traveler 𝑖

𝑃𝐸𝐷 𝑖 : ( 𝐹𝑃𝐸𝐷 𝑖 , 𝑃∗ 𝐸𝐷 𝑖 , 𝑃𝐸𝐷 𝑖 ) Penalty associated with early departure of traveler 𝑖 𝑃𝐿𝐴 𝑖 : ( 𝐹𝑃𝐿𝐴 𝑖 , 𝑃 ∗ 𝐿𝐴 𝑖 , 𝑃𝐿𝐴 𝑖 )

Penalty associated with late arrival of traveler 𝑖

𝑃𝐸𝐴 𝑖 : ( 𝐹𝑃𝐸𝐴 𝑖 , 𝑃 ∗ 𝐸𝐴 𝑖 , 𝑃𝐸𝐴 𝑖 )

Penalty associated with early arrival of traveler 𝑖

𝑃𝐿𝑇 𝑖 : ( 𝐹𝑃𝐿𝑇 𝑖 , 𝑃 ∗ 𝐿𝑇 𝑖 , 𝑃𝐿𝑇 𝑖 )

Penalty associated with activity duration lengthening of traveler 𝑖

𝑃𝐸𝑇 𝑖 : ( 𝐹𝑃𝐸𝑇 𝑖 , 𝑃 ∗ 𝐸𝑇 𝑖 , 𝑃𝐸𝑇 𝑖 )

Penalty associated with activity duration shortening of traveler 𝑖

𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝛿𝑆𝐼𝑛 : (𝛿𝐷𝐿,𝐸 , 𝛿𝐴𝑖,𝑡𝑟 𝐿,𝐸 , 𝛿𝑇𝐿,𝐸 ) Schedule inconsistency of type 𝐼𝑛 for trip 𝑡𝑟 of traveler 𝑖 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 ∆𝑆𝐼𝑛 : (∆𝐷𝐿,𝐸 , ∆𝐴𝑖,𝑡𝑟 𝐿,𝐸 , ∆𝑇𝐿,𝐸 ) Schedule inconsistency of type 𝐼𝑛 for trip 𝑡𝑟 of traveler 𝑖

𝑖,𝑡𝑟 ∆𝑆𝐼𝑛

=7

𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖 𝑖 𝐹𝑃𝐼𝑛 + 𝑃𝐼𝑛 ∗ 𝛿𝑆𝐼𝑛 𝛿𝑆𝐼𝑛 < 𝑇𝑆𝐼𝑛

𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖,𝑡𝑟 𝑖 𝑖 𝐹𝑃𝐼𝑛 + 𝑃𝐼𝑛 ∗ 𝛿𝑆𝐼𝑛 + 𝑃 ∗ 𝑖𝐼𝑛 ∗ (𝛿𝑆𝐼𝑛 − 𝑇𝑆𝐼𝑛 ) 𝛿𝑆𝐼𝑛 > 𝑇𝑆𝐼𝑛 𝑚𝑖𝑛 > (∆𝐷𝑡𝑟 + ∆𝐴𝑡𝑟 + ∆𝑇 𝑡𝑟 ) 𝑡𝑟 ∈𝜑 ′

𝑖

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Methodological Structure Step 0: Initialization (Time-dependent OD demand, time-dependent link pricing, VOT distribution, and initial path assignment, ,DTA Iteration=0, Iteration=1)

DTA Iteration= DTA Iteration+1

Step 1: Network Loading and Simulation: DYNASMART + NUTrans (Obtain link travel times and costs)

NO Step 3: DTA Convergence Checking Iteration=Iteration+1

Step 2: Path Set Generation and Path Assignment (Implement parametric analysis method (PAM ) to calculate Bi-criterion Time-Dependent Least Generalized Cost Path trees and corresponding VOT breakpoints)

YES

NO

Step 5: Convergence Checking

Step 4: Schedule Adjustment (find the descent direction: MSA based gap minimization)

YES Stop

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MULTI-‐MODAL DTA NU-‐TRANS

Transit Experience OMAZ-‐DMAZ Transit Sub-‐Tours by User Class

Inner Loop

Generalized Least Cost Paths for OTAP-‐DTAP

Chains with Given Trip Modes

Chain/ Tour Processor

Outer Loop

Level 2 Schedule Adj Connector Travel Times for PNR and KNR OMAZ-‐DMAZ Car Sub-‐Tours by User Class

ODT LOS and Experienced Trajectories (mulBmodal) Car Experience

Level 1 AcIvity & Schedule Planning/ Replan

Bus Link Travel Times

Dwell Times

ABM

Level 3 Real-‐Ime Schedule Adjustment

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Network ConfiguraIon

Large Scale Chicago Network

•  1961 Zones •  13093 Nodes • 40443 Links

• 36722 Arterials • 1400 Freeways

•  2000481 Vehicles loaded • 4864686 Total planned trips

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Gap Measures

Level 2 IntegraIon

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Level 2 IntegraIon

Results

Number of Households subject to schedule adjustment

12000 Random SelecIon Penalty Based

10000

UnrealisIc Only 8000

6000

4000

2000

0 0

2

4

6

8

10

12

Level 2 IteraBon Number

72

Level 2 IntegraIon

Results 3000

Number of Households with UnrealisBc Schedule

Random SelecIon Penalty Based

2500

UnrealisIc Only

2000

1500

1000

500

0 0

2

4

6

8

10

12


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Level 2 IntegraIon

Results 16

Random SelecIon

Average Inconsistent Schedule Penalty

14

Penalty Based UnrealisIc Only

12

10

8

6

4

2

0 0

2

4

6

8

10

12


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Conclusion •  Generalized Equilibrium Concept proposed with activity schedules: practical operational definition for integrating longterm ABM and DTA. •  Real-Time Activity Adjustment and Rescheduling: Important frontier in extending ABM logic into dynamic mechanisms for integration in DTA simulation.

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76

PREDICTIVE ANALYTICS:

Basis for Intelligent Control Strategies Consistent anBcipatory travel Bme InformaBon and rouBng decisions (Reference: Dong and Mahmassani, 2010, 2014)

Dynamic pricing for managed lane operaBons Link Toll Generator Predicted data

Toll values

Traffic Prediction

Real World Traffic Traffic data

(Reference: Dong et al. 2012) 77

PREDICTIVE ANALYTICS

Weather-‐sensiIve TrEPS Weather-‐sensiBve traffic operaBons model EsBmaBon: weather-‐sensiIve traffic simulaIon-‐assignment model

Weather data Weather monitoring systems

PredicBon: weather-‐sensiIve traffic simulaIon-‐assignment model

Weather forecast

Weather-‐responsive traffic management strategies

Alert weather condiBons

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Project ObjecIves Ø  Integrate and operaIonalize the weather-‐sensiIve TrEPS models calibrated for Salt Lake City to support weather-‐responsive traffic signal Iming implementaIon –  Evaluate different possible signal Iming strategies under weather-‐related scenarios –  Determine when to deploy such weather-‐responsive signal Iming plans

Ø  Monitor the implementaIon of the TrEPS-‐based decision support system, and its effecIveness in terms of weather-‐responsive traffic management

79

Real-‐Bme Surveillance Data §  Freeway detectors •  30-‐second observaIon interval •  occupancy, vehicle counts, speed

§  Riverdale road cameras •  Vehicle counts, speed 80

Real-‐Bme Traffic Management

81

PREDICTIVE STRATEGIES FOR REAL-‐TIME PICK-‐UP AND DELIVERY OPERATIONS (CITY LOGISTICS) Overall Architecture Real-Time Traffic Data and Events -Travel Times -Traffic Incidents

Dynamic Traffic Assignment Model and Simulator

Real-Time Requests

State Prediction Module

Online Booking Processor

A Priori Requests

A Priori Routing Planner

Service Network: Nodes: Unserved customers and NEWLY accepted customers, locations of fleets Links: time-dependent shortest paths linking nodes

Online Rerouting Planner

Lan and Mahmassani (2013, 2014) 82

A footnote– Trajectory Data











84

A Footnote: Trajectory Data Ø Collected by probe vehicles equipped with on board GPS devices Ø A trajectory is the path followed by the moving object through the spaIal area over which it moves 85

Trajectory Data Ø  InformaIon that can be extracted from trajectory data

–  from individual trajectory: •  •  •  •  •  •  •  • 

Time, i.e. posiIon of this moment on the Imescale; PosiIon of the vehicle in space; Trip origins and desInaIons ; DirecIon of the vehicle‘s movement; Speed of the movement; Dynamics of the speed (acceleraIon/deceleraIon); Accumulated travel Ime and distance. Individual path and temporal characterisIcs

–  from groups of trajectories:

•  DistribuIon of speed/travel Ime; •  Probe vehicle density; •  Inferred traffic volume.

86

2D Trajectories First car trajectory

1km

2D trajectories (along segment) have played essential role in development of traffic theories for individual highway facilities. However, in validation and application of traffic simulation models, the focus has been on measurements taken at a point (using fixed sensors) 87

3D Trajectories in a Network t

y destination

origin

destination

origin

x 88

Network 3D Time-Space Diagram t

y x

x y

3D trajectories of 1,000 simulated vehicles in Irvine, California Saberi, Mahmassani, Zockaie (2014)

89

Edie’s Definitions Extension to Networks

Courbon and Leclercq (2011) Saberi, Mahmassani, Zockaie (2014) t

d (ω ) Q(ω ) = Lxy (ω ) × Δt

3D shape ω

Δt y

t (ω ) K (ω ) = Lxy (ω ) × Δt

origin destination

x

where Q(ω) and K(ω) are the network-wide average flow and density for the specified shape ω; d(ω) is the total distance traveled by all the vehicles in the shape ω, t(ω) is the total time spent by all vehicles in the shape ω, Lxy(ω) is the total length (in lane-miles or lane-kms) of the network on the x-y plane associated with the shape ω, and Δt is the time height of the shape ω.

90

ACTIVITY PATTERN INFERENCE: Socio-demographic characteristics

Time 12 am

Home 7 pm

Model

5 pm

Grocery Shopping 3 pm 2 pm

School 10 am 8 am 5 am

Home

Z1

Space 91

Source: Mahdieh Allahviranloo

Z2

Z4

Z3 2

New era of trajectory-‐driven traffic and network performance analysis

–  More complete and compact descripIon of system state –  Capture all aspects of individual acIons (most complete record of actual behavior), with no loss of ability to characterize systems at any desired level of spaIal and temporal aggregaIon/disaggregaIon –  Retain ability to extract stochasIc properIes of both individual behaviors and performance metrics –  Enable bejer model formulaIon/specificaIon at all levels of resoluIon, and model calibraIon –  EffecIvely unify model calibraIon and network performance analysis –  Most promising hope to recognize and capture collecIve effects and interacIon mechanisms. 92

KEY TAKEAWAYS §  DTA has come a long way since the seminal work by Merchant and Nemhauser in 1978, both as a core topic in transportaIon science, as well as an essenIal component of the modern toolkit of transportaIon modelers for planning and operaIons applicaIons. §  Deeper insight into the various models’ properIes has been gained, and robust algorithms have emerged to compute equilibria and other fixed points of the models. §  At the same Ime, the boundaries of applicaIon have conInued to evolve through §  computaIon over larger-‐scale networks, §  integraIon with acIvity-‐based models (on the planning side), §  consideraIon of heterogeneous user preferences in applicaIons to wider range of policy quesIons and intervenIons (e.g. managed lanes, value pricing), and §  providing a core capability for real-‐Ime esImaIon and predicIon (for online operaIons).

§  Increasingly it is the tool of choice for analyzing impacts of new technologies, new service concepts, novel policies because DTA tools capture four criIcal phenomena: (1) Behavior, (2) Networks, (3) Conges8on, and (4) Dynamics. §  Yet agency pracIIoners are not totally on board §  Growing range of moIvaIng applicaIons raises many challenges– both fundamental and methodological, as well as pracIcal and implementaIon-‐related (devil is in the details). §  Successful applicaIon requires solid theory, and powerful methodological foundaIonal research moIvated by these challenges. 1/14/2013

93

KEY TAKEAWAYS

DTA DOES WORK IN PRACTICE!

1/14/2013

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