An Agent-Based Approach to Modelling Public
Transport Dynamics
Oded Catso.cats@tudelft.nlDelft
University ofTechnology

Challenge the future

Research Seminar, Tokyo University, 11-08-2015

OutlineConcepts
1. PT assignment principles
2. Modelling PT dynamics
3. Agent-based simulation modelApplications
1. Congestion
2. Real-time travel information
3. Service disruptions
4. Control and operational strategies

ResearchSeminar,TokyoUniversity,and11-08-2015
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1: Introduction
Urban network design

2

PTA principles and approaches

Research Seminar, Tokyo University, 11-08-20153

Frequency-based: Assignment principles• PT network is represented in terms of segments of lines• Demand is assigned based on service frequencies• Adopting concepts and solution methods from car traffic
assignment

Research Seminar, Tokyo University, 11-08-20154

Frequency-based: Network representation

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Urban network design5Schedule-based: Assignment principles• PT network is represented in terms of individual vehicle
trips/runs following a timetable• Demand is assigned to specific trips, takes into account timedependent characteristics• The concept of accumulative shortest path is not valid
anymoreResearchSeminar,
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CIE4811:PTND
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Urban network design6Schedule-based: Network representation

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Urban network design7

Schedule-based: Stop topology

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Urban network design8Traditional assumptions• Travel times is equal on all lines riding the same arc (FB)
• Passengers arrive randomly at stops• No capacity constraints• Perfect reliability (regularity – FB; punctuality – SB)• Passengers board the first arriving vehicle• Perfect infomration• Homogenous travellers’ population

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Flow-dependent in-vehicle timeFlow-capacity ratio multiplier• Already in the original presentation of optimal strategies• on-board crowding• Link travel time as a non-linear function of passenger flows• Iterative network loading to obtain equilibrium• BPR crowding function
run s  qa   1  run

 qa veh f

 s



arrrun, a  N dep,NAss

• qa / ( fℓs  ℓveh) is the saturation rate of the vehicle on the line
segment;• ℓrun and ℓrun are the BPR coefficient and exponent for running
congestion.
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Urban network design10Flow-dependent travel time
Effective frequency• Assigning weights to waiting times• Reliability effects and risk of denied boarding• An infinite penalty when capacity is exceeded• Reducing the nominal frequency by the BPR term qa  feffstwaitsfs

deparrrun,aN,NA
sswaitqa
1   wait  veh f s

0.5
 1   s  qa   eff
f s  qa ResearchSeminar,
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11

Does not guarantee that capacity is not exceeded!
Average VOC ratio drops from 4.77 to 1.5
Number of over-saturated line segments drops from 45 to 10

Cpeda et al. (2006)

ResearchSeminar,TokyoUniversity,and11-08-2015
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12Failure-to-board probability• FB: a quasi-dynamic model where the share of passengers
that exceeds the residual capacity on the respective time
period is transmitted to the next period• SB: guarantees that capacity constraints are satisfied at theindividual vehicle level by introducing new arcs between
successive vehicle trips
arrival node
dwelling arc
departure node

• Queuing(FIFO, mingling)running arc
boarding arc
alighting arc
Nℓsserv service nodefailure arcline nodestop nodebase nodequeuing arc
stop sstop arc

pedestrian arcs

base nodes

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13line ℓSeating and priorities• satisfy the set ofpriority rules and theseat capacity
constraint

Research
Seminar,
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14Main trends in developments of PT
assignment models (Liu et al 2010)• Consistently lagged behind developments in traffic modeling• Expected and emerging developments• Multi-agent simulation models• Dynamic loading process• Adaptive user decisions• Supply uncertainties

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2.
Agent-based approach to PTA

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Urban network design16Prominent research questions• How does the system perform under various conditions?
• How can APTS be deployed most effectively to improve seriveoperations?
• How to mitigate and manage service disruptions?
• How could service providers and users become more adaptive
by taking advantage of the abundance of real-time data?
• What is the impact of APTS measures?

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17Agent-based TAM• Represents individual vehicles and travellers• Emerging solution based on agents interaction with eachother throughout the simulation• En-route decisions• Day-to-day learning as proxy to equilbrium conditions• Integration with traffic simulation models

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Urban network design18Implementation: BusMezzo
Transit Assignment and Operations Simulation Model• A framework for analyzing transit performance undervarious operational conditions and APTS
• BusMezzo: integrated into Mezzo, a mesoscopic
traffic simulation model• Agent-based• Operations-oriented• Sources of uncertainty• Adaptive decision making• System level analysis

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A modelling framework for Analyzing
Public Transport Operations

NetworkService
Planning
Fleet

Passenger
Assignment

Traffic Dynamics &Transit Operations

DynamicLoading

Automated
Data Collection

Traveler
DecisionsDay-to-day
Within-day

TransitPerformanceControl
CentreReal-Time
Prediction

Traveler
Perception

Traveller
Strategy

Traveller
Population

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Network representation• Transit vehicle
trajectory• Ride• Queue• Dwell• Recover• Traveller
trajectory• Walk• Wait• On-board

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Public Transport Dynamics

Transit operations

Joint car and PT; mode-specifics
Dwell times
Fleet; vehicle scheduling
Crowding and capacity
Operations planning
Control and management strategies
Adaptive route choice
Real-time information

Transitperformance

Passengers
decisions

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Urban network design22Demand representation
Start• 𝜆𝑜𝑑 (𝑡, 𝜏) – Poisson arrival process• Non-compensatory rule-based choice-set
generation process• En-route decisions• Assess the attributes of each avilable

path

CONNETION
decision model

Arriving
transitvehicle

Boarding thisvehicle?

𝑣𝑖,𝑛 = 𝛽𝑖,𝑛 𝑋𝑖,𝑛• Calculate the joint utility of thebundled paths
𝑒 𝑣𝑖,𝑛𝑣𝐼,𝑛 = 𝑙𝑛𝑖∈𝐼BOARDING
decision modelYesApproachingtransit stop

ALIGHTING
decision model

Alighting at
the nextstop?

• Path: outcome of successive decisions• Preserve passenger integrity from one day
to the otherNo

NoYes
CONNETION
decision model

Arrived at
destination?

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Urban network designYes 23EndNo

Applications

Reliability andControl

Real-time
Information

Network
Resilience

Congestion
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Application: Increased capacity

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The dynamics of reliability & congestion• Route choice• Service reliability• Demand variation

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How can the value of reduced
congestion be quantified?

Research Seminar, Tokyo University, 11-08-201527

Evaluation of congestion effects
On-board crowding

Increased preceived in-vehicle time

Denied boarding

Increased waiting time

Reduced service relaibility

Increased total travel time

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28

Appraisal of Increased Capacity• Crowding factor in static/dynamic model: +3%/+60%• Value of increased capacity: underestimated in static models• Overestimation in BusMezzo: currently incorporate crowdingin the route choice modelResearch Seminar, Tokyo University, 11-08-2015

29

Real-time Travel Information:
Predicting, disseminating, rerouting

ResearchSeminar,
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Oded
CatsPTND
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2014
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andUrban network design30Modelling Impacts of Information

Performance
Prediction
Provision

Perception

Path choice
ResearchSeminar,
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CatsPTND
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andUrban network design31Passengers’ Response to Service
Reliability and Travel Information

ResearchSeminar,TokyoUniversity,
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CatsPTND
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andUrban network design32Day-to-Day Learning of Service andInformation Reliability
Final distribution of credibility coeff.

Example: evolution of credbility coeff.
credibility coefficients - disaggregate analysis
1

end of the learning period
frequency

0.4

0.9
0.2

0.8
00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.7

alphaRTI
frequency

0.4

0.6
0.5

0.2

0

alphaRTI
alphaEXP
alphaPK

0.4
00.1

0.2

0.3

0.4

0.50.6

0.7

0.8

0.9

1

alphaEXP

0.3

frequency

0.4

0.2
0.2

0.1
00

0.1

0.2

0.3

0.4

0.5

alphaPK

0.6

0.7

0.8

0.9

102468101214

16

18

20

22

day

ResearchSeminar,
TokyoUniversity,
11-08-2015
Oded
CatsPTND
seminar,MIT,
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2014
CIE4811:
1: Introduction
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24

Disruptions: impact and implications
for strategic planning and operational
management

Research Seminar, Tokyo University, 11-08-201534

What is the Weakest Link?
• Main determinants ofnetwork robustness?
• Potential benefits of realtime information
dissemination?

Hötorget
Alvik

Centralen
Fridhemsplan

SlussenHornstull

Liljeholmen

Gullmarsplan• How incorporate
vulnerability into network
planning decisions?
• Requires non-equilbrium
assignment

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Capturing disruption dynamics• Static model: underestimation of disruption effects• En-route decisions, imperfect information• Both passengers and operators can respond to disruptions

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Criticality: Relative welfare loss

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Value of Real-time information:
Relative welfare gain

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Normal operations

Disruption (D4)

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39

Evaluation framework
Base Case(Central Links
Disruption(Disruption

Important Links
Overloaded Links
Capacityenhancement( ,h)Capacityenhancement

Capacityenhancement

Capacityenhancement

Effective Capacity Enhancement Scheme
Research Seminar, Tokyo University, 11-08-2015

PBC
Disruption∆𝑊
𝑉𝑂𝐶, ∆𝑉𝑂𝐶

𝑉𝑆𝐷𝑀
40VOC change due to disruptions

Disruption on 10-11, southboundDisruption on 13-14, southboundResearch Seminar, Tokyo University, 11-08-2015

41

Where shall we increase capacity?

+9%
Hötorget

+6%

Alvik

+2%
Centralen

Fridhemsplan

+3%

+16%

+6%
SlussenHornstull

Liljeholmen

Research Seminar, Tokyo University, 11-08-2015

Gullmarsplan

42Impact indicators

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43

Evaluation example

No

Yes

Value ofstrategic
disruption
mitigationNo𝑤(0,0)𝑤(𝛿, 0)+7.06%

Yes

𝑤(0, ℎ)𝑤(𝛿, ℎ)+2.77%

Value of capacity
enhancement-24.67%-27.69%(planned)

Disruption (D-Blue)

Capacityenhancement(C-Green)

R – Stop-level

Research Seminar, Tokyo University, 11-08-2015

44Beyond a complete failure• Most disruptions do not amount to complete breakdowns(maintenance and construction works, traffic incidents or cancelled services)• Vulnerable systems - greater negative impacts in a disproportional
relation to the increase in the original capacity reduction• Non-linear properties of network
effects, traffic dynamics and route
choice -> non-trivial relation?

Vulnerable• Systems that operate close tocapacity• Line-level; full-scan; dynamic
assignment
Research Seminar, Tokyo University, 11-08-2015

45

Relation between capacity reduction
and change in societal cost• Long and small rather than short and large capacity reductions• The same capacity increase counts more when relieving a larger
capacity reduction
Research Seminar, Tokyo University, 11-08-201546

On-going research• Modelling Day to day congestion equilibrium conditions
 Habit formation and limited adaptation
 Passenger groups Real-time dynamic control optimization• Applications
 Transfer coordination strategies
 Fleet management strategies
 Paris and Amsterdam networks

Research Seminar, Tokyo University, 11-08-201547

Thank you! Questions?

o.cats@tudelft.nl
odedcats.weblog.tudelft.nl

ResearchSeminar,
Tokyo
University,
11-08-2015
Oded
CatsPTND
seminar,MIT,
20 Nov
2014
CIE4811:
1: Introduction
andUrban network design48