Enlarging the Options
in the Strategy-based Transit Assignment
Isabelle Constantin and Michael Florian
INRO
TRB Applications Conference
Reno 2011
Contents
Motivation
Computing logit choice of strategies
Distribution of flow between connectors
Distribution of flow between attractive lines
Conclusions
TRB Applications Conference
Reno 2011
Strategy-based Transit Assignment
The optimal strategy algorithm is well understood
and field tested
Extended successfully to congested transit
assignment and capacitated transit assignment
Further extensions can provide a richer set of
transit modeling features
TRB Applications Conference
Reno 2011
Deterministic vs Stochastic Strategies
Currently in an optimal strategy
All the flow at a node either
1. leaves by the best walk link, or
2. waits at the node for the first attractive line to be served
Logit choice of strategies
A logit model can be used to distribute the flow at a node
between ride and walk options:
1. leaving by the best walk link or other “efficient” walk links
2. waiting at the node for the first “efficient” line to be served
TRB Applications Conference
Reno 2011
Adding a Walk-to-line Option: a Small Example
25 minutes
Line Headway
12 min
O
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
The demand from O to D is 100
TRB Applications Conference
Reno 2011
6 min
The Optimal Strategy
50 trips
Line Headway
12 min
O
D
12 min
30 min
41.67 trips
50 trips
A
B
8.33 trips
Expected travel time 27.75 min
TRB Applications Conference
Reno 2011
6 min
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
15 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
New walk path is 26 min
TRB Applications Conference
Reno 2011
6 min
10 min
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
15 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
First strategy time is 27.75 min
TRB Applications Conference
Reno 2011
6 min
10 min
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
15 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
Second strategy time is 26.00 min
TRB Applications Conference
Reno 2011
6 min
10 min
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
15 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
New walk path is 26 min (vs 27.75 min)
Optimal strategy is to walk to the orange line
TRB Applications Conference
Reno 2011
6 min
10 min
Logit Choice of Strategies
22.9 trips
Line Headway
12 min
O
E
54.2 trips
D
12 min
30 min
3.82 trips
22.9 trips
A
6 min
B
10 min
19.08 trips
Logit choice of strategies (with scale = 0.1)
First strategy
45.8 trips
Second strategy
54.2 trips
TRB Applications Conference
Reno 2011
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
17 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
The travel time of the orange line is
increased by 2 minutes to 17 minutes
TRB Applications Conference
Reno 2011
6 min
10 min
Logit Choice of Strategies
25 minutes
Line Headway
12 min
6 min
O
E
17 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
Second strategy time is now 28.00 min
TRB Applications Conference
Reno 2011
6 min
10 min
Adding a Walk-to-transit Option
25 minutes
Line Headway
12 min
6 min
O
E
17 min
D
12 min
30 min
10 min
6 min
7 min
B
A
4 min
4 min
New walk path is 28 min vs 27.75 min
Optimal strategy does not use the walk
to the orange line
TRB Applications Conference
Reno 2011
6 min
10 min
Logit Choice of Strategies
25.3 trips
Line Headway
12 min
O
E
49.4 trips
D
12 min
30 min
4.2 trips
25.3 trips
A
6 min
B
10 min
21.1 trips
Logit choice of strategies (with scale = 0.1)
First strategy
45.8 50.6 trips
Second strategy
54.2 49.4 trips
TRB Applications Conference
Reno 2011
Contents
Motivation
Computing logit choice of strategies
Distribution of flow between connectors
Distribution of flow between attractive lines
Conclusions
TRB Applications Conference
Reno 2011
How Can One Enlarge the Choice Set?
Option 1
Generate a set of paths by O-D pair prior to the
execution of the route choice algorithm
Drawbacks


the paths are generated by using heuristics,
so the path choices are somewhat arbitrary
the paths are processed by O-D pair,
so the computation time increases as the square of the
number of zones
TRB Applications Conference
Reno 2011
How Can One Enlarge the Choice Set?
Option 2
Enlarge the set of walk links and transit line segments
that are considered in the transit assignment by using
a well defined criterion
Advantage

This preserves the computations by destination,
so the computation time increases only linearly
with the number of zones
This is the approach that we have chosen
TRB Applications Conference
Reno 2011
Modified Strategy Computation
The optimal strategy algorithm is first modified to
compute simultaneously at each node two values:
The best expected travel and wait times from a node to
the destination either:

by boarding a vehicle at the node, and

by walking to another node(stop) to board a vehicle.
TRB Applications Conference
Reno 2011
Modified Strategy Computation
Then, any “efficient arcs” or “efficient line segments"
are included, in addition to those of the optimal strategy,
by using the criteria:

a walk arc is efficient if, by taking it,
one gets nearer to the destination

a transit segment is efficient if, by boarding it,
the best alighting stop is nearer to the destination
Node likelihoods are computed recursively in order to obtain
the probabilities (proportions) of all the strategies included
TRB Applications Conference
Reno 2011
Another Example
The demand is 100 in each direction
TRB Applications Conference
Reno 2011
Another Example: Optimal Strategy
TRB Applications Conference
Reno 2011
Logit Choice of Strategies
Scale: 0.2
TRB Applications Conference
Reno 2011
Distribution of Flow Between Connectors
There is another way to ensure that more than one
connector is used to access the transit services:

Apply the logit choice only to the connectors by considering
the length of each connector and the expected travel time to
destination from the accessed node
TRB Applications Conference
Reno 2011
Logit Choice Only on Connectors
Scale: 0.2
TRB Applications Conference
Reno 2011
Cut-off: 0.01
Another Example: Optimal Strategy
TRB Applications Conference
Reno 2011
Distribution of Flow – Increased Tram Time
Optimal strategy when eastbound tram time is increased
TRB Applications Conference
Reno 2011
Distribution of Flow – Increased Tram Time
Logit on strategies when tram ride time is increased
TRB Applications Conference
Reno 2011
Distribution of Flow – Increased Tram Time
Logit choice only on connectors
TRB Applications Conference
Reno 2011
Contents
The issues that are addressed
Computing logit choice of strategies
Distribution of flow between connectors
Distribution of flow between attractive lines
Conclusions
TRB Applications Conference
Reno 2011
Distribution of Flow Between Attractive Lines
Optimal strategy assignment:
the flow at a transit node is distributed based on frequency
p l = fl / f
where f = sum of the frequency of the attractive lines
Suboptimal strategy taking into account line travel times:
the flow at a transit node can also be distributed based on
frequency and time to destination by giving priority to the
faster lines
pl = p_adjustl * fl / f
t  average_t
where the adjustment factor is computed as p_adj l  1 wait
and the fastest line is considered first
l
TRB Applications Conference
Reno 2011
Distribution of Flow Between Attractive Lines
Optimal Strategy
TRB Applications Conference
Reno 2011
Distribution of Flow Between Attractive Lines
Logit choice of strategies and transit time to destination
TRB Applications Conference
Reno 2011
Contents
Motivation
Logit choice of strategies
Distribution of flow between connectors
Distribution of flow between attractive lines
Conclusions
TRB Applications Conference
Reno 2011
Enhanced modeling possibilities
The consideration of a richer set of strategies
Inclusion of walk in “sub-optimal” strategies
Modeling of uneven population distribution in
large zones
Evaluation measures based on log-sum
computations
Without losing any computational efficiency
…
TRB Applications Conference
Reno 2011