Estimating Passengers’ Path Choices Using Automated Collection Data in

Urban Rail Systems

Zhenliang (Mike) Ma

Baichuan Mo, Haris N. Koutsopoulos, Yiwen Zhu, Yunqing Chen

2

Crowding

• Issues and challenges

‒ Near capacity operations

‒ Passengers’ denied boarding

‒ Safety

• Passengers’ perception of crowding‒ In-vehicle: 1 min standing (up to 10 min) = 2.04 min uncrowded seating*

*Zheng Li, David A. Hensher, Crowding and public transport: A review of willingness to pay evidence, Transport Policy, 20113

Building Blocks for Transit Data Analytics

• Customer experience• Denied boarding• Reliability

• System performance• Crowding

Monitoring

• Route choice• Habitual• Interventions • Disruptions• Information

Behavior • Real-time prediction• Demand• Individual mobility

• Strategic planning• TDM • NPM (assignment)• Micro-simulation

Prediction & Planning

4

Problem Definition

• General methodology to estimate the route choice fractions of OD pairs and discrete choice model parameters at different time periods considering crowding impacts using AVL and AFC data in the system

AFCAVL

Network

1 2

330%

70%

𝛽𝑡𝑟𝑎𝑣𝑒𝑙_𝑡𝑖𝑚𝑒

𝛽𝑤𝑎𝑖𝑡_𝑡𝑖𝑚𝑒

𝛽𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟_𝑡𝑖𝑚𝑒

……5

Mo

nito

ring

Plan

nin

g

• Platform crowding / denied boarding

• Route choice behavior

Impacts of Crowding on Passengers

A

C

E D

B

6

Passenger OD Journey Time Distribution

A

C

B

7

Challenges

8

Run times + Walking times

Pro

bab

ilit

y

Waiting times

Pro

bab

ilit

y

Journey times

Pro

bab

ilit

y

• A passenger with a long journey time – chose a longer route, or – denied boarding multiple times on a shorter route

Observed

9

Approach Data Level Applications Characteristics

Passenger-to-Itinerary-Assignment(Zhu et.al. 2018)

AFC (tap-in & out)AVLWalk distance/speed

Station Performancemeasurement

Needs access/egress time distributions

Sensitive to model parameters

Unsupervised learning

5-10 mins to run

Structured Mixture Model(Ma et.al. 2019)

AFC (tap-in & out)AVL

Station Performance measurement

No external data neededUnsupervised learning2-5 seconds to run

Regression(Miller et.al. 2018)

AFC (tap-in)AVLDenied boarding observations

Station Performancemeasurement

Prediction

Requires observations of denied boarding for calibration Supervised learning

NetworkAssignment(Ma et.al. 2019)

OD flows Path choice fractionsAVLCapacity

Network Performancemeasurement

Planning

Applied at the network level

Various crowding metrics

Requires capacity

Overview: Denied Boarding Approaches

10

Overview: Path Choice Approaches

Model Data Applications Characteristics

AFC AVL Monitor Planning OD path

fraction

Individual

choice

Crowding Probabilistic

model

Intera

ctions

Sun et al (2016)

J. Zhao et al (2017)

√ √ √ √ √ √

Sun et.al. (2015)

Zhang et.al. (2018)

√ √ √ √ √ √

Hörcher, et al. (2017) √ √ √ √ √ √ √

OD Journey time based

approach

√ √ √ √ √ √ √ √

Network based

approach

√ √ √ √ √ √ √ √ √

Denied Boarding Estimation

11

• AFC and AVL data for a given OD pair (with no transfer and no route choice).• The origin is the station of interest for which denied boarding metrics will be

estimated

Ma et. al, 2019

Structured

Path Choice Estimation: MLE Formulation

maxmize𝜷

𝐿𝐿 𝑥1, 𝑥2, … , 𝑥𝑁; 𝜷, 𝑻 = 𝑙𝑜𝑔

𝑛∈𝑁

𝑃 𝑥𝑛; 𝜷, 𝑻

=

𝑛∈𝑁

𝑙𝑜𝑔

𝑚∈𝑀𝑛

𝑃 𝑥𝑛|𝑚; 𝑻 × 𝜋ℎ𝑚

where ∶𝜋ℎ

𝑚 : Path fraction for route m at time period h

𝑥𝑛 : Observation of journey time of a passenger𝑚 : Path 𝑚 for passenger 𝑛𝒛ℎ𝑚: Attribute vector for path 𝑚 at time period h (e.g. travel time, crowd, etc.)

T : Train run times (i.e. arrival and departure time from platform)𝜷 = 𝛽1, 𝛽2, … , 𝛽𝑀 : Unknown parameters to be estimated

𝜋ℎ𝑚 =

𝑒𝑥𝑝 𝜷𝒛ℎ𝑚

𝑚′=1𝑀 𝑒𝑥𝑝 𝜷𝒛ℎ

𝑚′

12

Probabilistic Process

𝑃 𝑥𝑛|𝑚; 𝑻

13

Time-Space Diagram and Itineraries

Entry gate Origin platform Destination Platform

Tap-in

Access time

Space

Exit gate

Tap-out

Egress timeLine 1

Transfer Platform

Transfer time

Line 2Time

14

Likelihood of an Observation Given a Path

𝑃 𝑥𝑛|𝑚; 𝑻 = P 𝑡𝑖𝑛, 𝑡𝑜𝑢𝑡|path =

itinerary

P 𝑡𝑖𝑛, 𝑡𝑜𝑢𝑡 𝑖𝑡ℎ itinerary

=

Itinerary

P 𝑎𝑐𝑐𝑒𝑠𝑠 𝑖𝑡ℎ itinerary ∗

𝐽

P 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑗 𝑖𝑡ℎ itinerary ∗ P 𝑒𝑔𝑟𝑒𝑠𝑠 𝑖𝑡ℎ itinerary

𝑙=0

𝐿

P 𝐷𝑒𝑛𝑖𝑒𝑑𝑙| 𝑖𝑡ℎ itenerary ∗ P 𝑡𝑙𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟

𝑘=0

𝐾

P 𝐷𝑒𝑛𝑖𝑒𝑑𝑘| 𝑖𝑡ℎ itenerary ∗ P 𝑡𝑘𝑎𝑐𝑐𝑒𝑠𝑠

P 𝑡𝑒𝑔𝑟𝑒𝑠𝑠| 𝑖𝑡ℎ itenerary

The denied boarding, access time, transfer time and egress time distributions can be pre-calculated based on AFC and AVL data or from survey data. (Zhu, 2017) 15

Model Characteristics

maxmize𝜷

𝐿𝐿 𝑥1, 𝑥2, … , 𝑥𝑁; 𝜷, 𝑻 = 𝑙𝑜𝑔

𝑛∈𝑁

𝑃 𝑥𝑛; 𝜷, 𝑻

=

𝑛∈𝑁

𝑙𝑜𝑔

𝑚∈𝑀𝑛

𝑃 𝑥𝑛|𝑚; 𝑻 × 𝜋ℎ𝑚

=

𝑛∈𝑁

𝑙𝑜𝑔

𝑚∈𝑀𝑛

𝑐𝑚,𝑛

𝑒𝑥𝑝 𝜷𝒛ℎ𝑚

𝑚′∈𝑀𝑛𝑒𝑥𝑝 𝜷𝒛ℎ

𝑚′

=

𝑛∈𝑁

𝑙𝑜𝑔1

𝑚′∈𝑀𝑛𝑒𝑥𝑝 𝜷𝒛ℎ

𝑚′

𝑚∈𝑀𝑛

𝑐𝑚,𝑛𝑒𝑥𝑝 𝜷𝒛ℎ𝑚

Model Characteristics

𝑛∈𝑁

𝑙𝑜𝑔1

𝑚′∈𝑀𝑛𝑒𝑥𝑝 𝜷𝒛ℎ

𝑚′

𝑚∈𝑀𝑛

𝑐𝑚,𝑛𝑒𝑥𝑝 𝜷𝒛ℎ𝑚

=

𝑛∈𝑁

−𝑙𝑜𝑔

𝑚′∈𝑀𝑛

𝑒𝑥𝑝 𝜷𝒛ℎ𝑚′

+ 𝑙𝑜𝑔

𝑚∈𝑀𝑛

𝑐𝑚,𝑛𝑒𝑥𝑝 𝜷𝒛ℎ𝑚

LogSumExp Function is convex-LogSumExp Function is concave

• This problem is known as DC (Difference of Convex) Programming• DCP can be solved globally by methods such as branch and bound, which may be

slow in practice. A locally optimal (approximate) solution can be found through the many techniques of general nonlinear optimization. (Shen et. al 2016)

Implementation

• Select OD pairs

• Prepare inputs• Denied boarding distribution (Ma et.al, 2019)

• Approximated walking distance (station layout)

• Walking speed distribution (Zhu et.al, 2017)

• Path attributes (network)

• Solve the MLE problem

18

Case Study Using Synthetic Data

52

3

14

67

3 m

in

2 min2 min2 min

3 m

in3

min

3 m

in

• Network– Walk distance 30-50 m (access, egress,

transfer)• Train operations

– Headway 2 min– Headway deviation (-10, 10) sec– Trave time deviation (-20, 20) sec

• Passengers– Walk speed distribution, logn(0.1, 0.4)

– Mean 1.2m/s, std 0.25m/s– Denied boarding at station 2

– Distribution (0.2, 0.5, 0.3)

19

Setting

Jin, F., Yao, E., Zhang, Y., & Liu, S. (2017). Metro passengers' route choice model and its application considering perceived transfer threshold. PloS one, 12(9)

Variables Beta values

In_Veh_Time -0.246

Out_Veh_Time -0.439

No_of_Transfers -1.707

Denied_Waiting -0.480

52

3

14

67

9 OD Pairs:{1, 5, 4} -> {3, 6, 7}

20

𝑉𝑖 = 𝛽1𝐼𝑛_𝑉𝑒ℎ_𝑇𝑖𝑚𝑒𝑖 + 𝛽2𝑂𝑢𝑡_𝑉𝑒ℎ_𝑇𝑖𝑚𝑒𝑖 + 𝛽3𝑁𝑜_𝑜𝑓_𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑖 + 𝛽4𝐷𝑒𝑛𝑖𝑒𝑑_𝑊𝑎𝑖𝑡𝑖𝑛𝑔𝑖

0,00

0,20

0,40

0,60

0,80

1,00

1_3 5_3 4_3 1_6 5_6 4_6 1_7 5_7 4_7

Path_1 Path_2

True path share for OD pairs

Results: Denied Boarding Estimation

21

0

0,1

0,2

0,3

0,4

0,5

0,6

0 1 2

Pro

abil

ity

Denied boarding times

TRUE

ESTIMATE

Results: Discrete Choice Model Parameters

Variables Beta values (true) Beta values (estimated)

In_Veh_Time -0.246 -0.201

Out_Veh_Time -0.439 -0.411

No_of_Transfers -1.707 -1.548

Crowd_Waiting -0.48 -0.525

0,00

0,20

0,40

0,60

0,80

1,00

1_3 5_3 4_3 1_6 5_6 4_6 1_7 5_7 4_7

Pat

h_1

Fra

ctio

n

OD Pairs

TRUE

ESTIMATION

Sensitivity Analysis: Parameter Initialization

23

-1,8

-1,6

-1,4

-1,2

-1

-0,8

-0,6

-0,4

-0,2

0E

stim

ated

par

amet

ers

Difference between initialization and true parameters

beta_tt

beta_ovt

beta_not

beta_cw

0 0.5 1.0 1.5 2.0 2.5 3.0

Sensitivity Analysis: Denied Boarding

24

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

1_3 5_3 4_3 1_6 5_6 4_6 1_7 5_7 4_7

Pat

h_1

fra

ctio

n

OD pairs

TRUE

SET1

SET2

SET3

Denied Set_1 Set_2 Set_3

0 0.2 0.2 1

1 0.5 0.6 0

2 0.3 0.2 0

Sensitivity Analysis: Walking Speed

25

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

1_3 5_3 4_3 1_6 5_6 4_6 1_7 5_7 4_7

Pat

t_1

fra

ctio

n

OD pairs

TRUE

SET1

SET2

Mean Std

Set_1 1.2m/s 0.5m/s

Set_2 1.4m/s 1m/s

Summary

• Probabilistic model for path choice estimation considering denied boarding at key stations• Flexible to incorporate different variables and model structures

• Robust to parameter initialization and small errors in inputs

• Neglecting denied boarding can lead to biased estimation of path fractions

• Future work• Real-world data testing

• Learning behaviour under intervention (e.g. network expansion)

26

Zhenliang(Mike) Ma

mike.ma@monash.edu

https://www.monash.edu/engineering/mikema

27

Network Based Path Choice Estimation

28

Initial parameters and OD entry demand

NPM Engine (Assignment)

OD exit flows

Difference between model and “true” OD exit flows is small enough

No

, up

dat

ep

aram

eter

s

Path choice parameters

Simulation based optimization

Preliminary results (Bayesian method)

29

Variable Beta (true) Beta (Estimate)

In vehicle time -0.0663 -0.0798

# of transfer -0.438 -0.293

Transfer time -0.183 -0.210

Commonality Factor -0.941 -0.996

Map distance -0.0767 -0.0671

• Synthetic data generated using MTR network

Discrete choice model provided by MTR using 2012 survey

Preliminary results (Bayesian method)

30

Best point

‘Brute-force’

Analytical Model

31

𝛽 is the prior parameters for the choice model

𝑞𝑟𝑖𝑚𝑗𝑛 is the observed OD

entry-exit flow.

Nonlinear equation constraints

Non-analytical constraints

Final Model Formulation

32

Preliminary Test (Small Network)

33