2016 IEEE 19th International Conference on
Intelligent Transportation Systems (ITSC 2016)
Route choice in public transport networks:
choice set generation and route choice models
Shlomo Bekhor
Technion - Israel Institute of Technology
November 2016
Background
• Transit assignment or simulation require some
behavioral assumptions regarding the
passenger’s route selection.
• An inter-related problem is the generation of
alternative routes
•
•
•
•
Accounting for the complexity of different trip legs:
walking to or from the station,
waiting and riding transit lines,
perhaps transferring between them.
• People have different time perceptions of these
components.
Overview
• This presentation is composed of two parts:
1. Choice set generation approaches
• Methods that can be applied for real-size networks.
2. Transit route choice models in the
assignment and simulation contexts.
Two types of choice behavior
1. Pre–trip choice: made before starting the trip
• Continuous service systems (transit and pedestrian
networks) without unexpected events
2. En-route choice: made during the trip, to
adapt to random or unknown events
• Route systems with unexpected events
• En-route information
• Route choice models assume either pre-trip or
mixed pre-trip/en-route choice behavior
• Depending on the characteristics of the
transportation service they are applied to.
4
Alternative modeling
approaches
• Temporal consideration
• Static (frequency-based)
• Dynamic (timetable or schedule-based)
• Personal consideration
• Aggregate level (transit assignment)
• Individual level (simulation)
• Equilibrium consideration
• Ignore congestion
• Defer to board crowded vehicle
• Iterative approach
5
Classification of PT services
(Cascetta, 2001)
• Frequency:
• Low: av. headway > 30 mins (e.g. non-urban transit
services)
• High: av. headway <12-15 mins (urban transit)
• Regularity:
• Low (e.g. urban transit services): average delays
“large” compared to the average headways
• High (e.g. airlines, intercity train services) : average
delays “small” compared to the average headways
Route Choice Models:
Two-stage Choice Process
1. Choice Set Generation
2. Route Choice Given a Choice Set
7
Choice Set Generation Models
exhaustive
selective
stochastic
deterministic
probabilistic
K-shortest paths
STOCH (Dial, 1971)
Formulation (Manski,1977)
penalty / elimination
Simulation of link
attributes (FiorenzoCatallano, 2001)
Choice Set Indicators
Labeling (Ben-Akiva
et al.,1984)
Hybrid (Baaj and
Mahmassani, 1994)
Constrained enumeration
(Friedrich et al., 2001)
(Ben-Akiva and Boccara,1995)
Availability Model
(Cascetta et al,1998)
Gravity approach
(Bagloe and Ceder, 2011)
Simulation of Link Attributes
Network Topology
Random Link Costs
Shortest Path
The same route
may be found
several times
during the
iterative process
Add to Choice Set
Nielsen (2000)
Bekhor et al. (2001)
Fiorenzo-Catalano and Van der Zijpp (2001)
Bierlaire and Frejinger (2005)
Bovy and Fiorenzo-Catalano (2006)
9
Link (Route) Elimination Method
Network Topology
Shortest Path
The same route
may be found
several times
during the
iterative process
Add to Choice Set
Delete Link (Route)
Azevedo et al. (1993)
Bekhor et al. (2001)
Prato and Bekhor (2006)
Frejinger and Bierlaire (2007)
Schussler et al.
(2010)
Breadth-First
Search
10
Example: Winnipeg network
(Bekhor et al., 2006)
50 routes generated for a single OD pair using the
link elimination method
Branch and Bound Method
(Friedrich et al., 2001)
• A segment is inserted to the tree if and only if
all the following conditions hold:
• Temporal suitability: the connection departs the
node only after the arrival of a connection plus a
minimum transfer wait time
• Dominance: exclude segments with both early
departure and late arrival times
• Tolerance constraint: excludes paths with
unrealistic travel times
• Loop constraint: remove paths with large detours
12
Structure of the connection
tree (Friedrich et al., 2001)
Evaluation of Path Generation
Algorithms
• Coverage: generated route matches the observed route at a
specified threshold (Bovy, 2007):
 Lng



I


I Ong     

n 1  Ln

 n 1

N obs
N obs
N obs
Cg 
N cov
N obs
N obs
• Variety: generated routes should not overlap “too much”
• Variance: generated routes should not exceed a certain threshold
with respect to different attributes
• Note – for dense networks, it is reasonable to evaluate coverage
at the route level, regardless of the specific boarding and
alighting stops of the observed route.
14
Example: Paris network
(van der Gun, 2013)
Branch and Bound method
Criterion
Exact matching
Same mode and line
Dominance
Total matched
No match
Total observations
Number of
routes
Percentage
361
423
610
1394
227
1621
22%
26%
38%
86%
14%
100%
Example: Copenhagen network
(Anderson, 2013)
Simulation method - coverage for link and stop levels
Choice set generation
comparison (large networks)
Coverage
Variety
(nonoverlapping)
Variance (with
respect to
shortest path)
K-shortest path
Low
Low
Low
penalty/elimination
Low
Medium
Medium
Medium
High
Medium
High
High
Medium
Simulation
(low variance)
Medium
Low
Low
Simulation
(high variance)
High
Medium
Medium
Method
Labelling
Branch and bound
Transit assignment models
• Different modeling approaches -
• Reviews by Liu et al.(2010), Cats (2011), Fu et al. (2012)
Equilibrium
Consideration
No
Temporal
Consideration
Yes
No
Yes
?
Frequency-based assignment
models – uncongested
• Passenger arrives at random to the stops
• Deterministic headways
• Analytical solution
•
•
•
•
•
Trunk lines (Dial, 1967)
Common line dilemma (Chriqui and Robillard, 1975)
Passenger arrival process (Marguier and Ceder, 1984)
Hyperpath concept (Nguyen and Pallotino, 1988)
Optimal Strategies (Spiess and Florian, 1989)
• Implemented in transportation software
Frequency-based assignment
models accounting for congestion
• De Cea and Fernandez (1993) - high probability
to denied boarding for low effective frequency
• Wu et al. (1994) – UE formulation
• Lam et al. (1999) – SUE formulation
• Nielsen (2000) – MSA algorithm
• All models above – still static in nature
Schedule-based assignment
models
• Time-space graphs : Nuzzolo and
Russo (1996) Cascetta (2001),
Nuzzolo and Crisalli (2004)
• Service represented by individual
vehicle runs following a given
timetable
• Passenger demand segmented in
time intervals
• Capacity constrained:
Schmoker,2006; Zhou et al.,
2008; Sumalee et al., 2009;
Zhang et al., 2010
Simulation models
• Wahba and Shalaby (2006) - micro-simulation
learning-based approach
• Rieser et al. (2009) – agent-based simulation
• Toledo et al. (2010) - mesoscopic simulation
for transit operations
• Cats (2011) - Dynamic modelling of transit
operations and passenger decisions
Random Utility Models
• Multinomial Logit (MNL) – most common
• Hunt (1990), Guo (2011), Cats (2011), Khani et al. (2014)
• Path-Size logit (PSL) – account for overlapping
• Hoogendoorn-Lanser et al. (2005)
• Mixed Logit – Eluru et al. (2012)
• Parameter estimation based on revealed
preference surveys
• Usual variables – level-of-service attributes
• Raveau et al. (2011) and Guo (2011) – transit map
attributes
Example: Austin, TX data
(Khani et al., 2014)
Source data – 6,528 observations from an on-board survey
Parameter
Ratio to in-vehicle
time
In-vehicle time (min)
-0.0733
1.0
Waiting time (min)
-0.208
2.8
Walk time (min)
-0.767
10.5
walk time (frequent users)
-0.537
7.3
Number of transfers
-5.92
80.8
-0.936
12.8
1.19
-16.2
Attribute
Paid fare ($)
Regional route indicator
Example: Haifa data (Cats, 2011)
Source data – 2,524 observations from a web-based survey
Parameter
Ratio to in-vehicle
time
In-vehicle time (min)
-0.047
1.0
Waiting time (min)
-0.093
1.9
Egress time (min)
-0.0907
1.8
Number of transfers
-0.371
7.5
Available seat indicator
0.539
-10.8
Schedule adherence (%)
0.0528
-1.1
Denied boarding (%)
0.0345
-0.7
Attribute
Summary
• Choice set generation methods – usually based
on heuristic methods
• Route choice models – less developed in
comparison to models developed for private car
• Frequency-based models – still useful for
planning purposes
• Equilibrium consideration – open
Thank you…