enlarging the options in the strategy-based transit assignment
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Enlarging the Options in the Strategy-based Transit Assignment. Isabelle Constantin and Michael Florian INRO. Motivation Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions. Contents. - PowerPoint PPT PresentationTRANSCRIPT
Enlarging the Options in the Strategy-based Transit Assignment
TRB Applications Conference Reno 2011
Isabelle Constantin and Michael FlorianINRO
TRB Applications Conference Reno 2011
Motivation Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions
Contents
TRB Applications Conference Reno 2011
Strategy-based Transit Assignment
The optimal strategy algorithm is well understood and field testedExtended successfully to congested transit assignment and capacitated transit assignmentFurther extensions can provide a richer set of transit modeling features
TRB Applications Conference Reno 2011
Deterministic vs Stochastic Strategies
Currently in an optimal strategyAll 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
servedLogit choice of strategiesA 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
12 min 12 min 30 min 6 min
Headway
4 min
7 min
25 minutes
6 min 10 min
4 min
O
A
D
B
Line
The demand from O to D is 100
TRB Applications Conference Reno 2011
The Optimal Strategy
12 min 12 min 30 min 6 min
Headway50 trips
50 trips 41.67 trips
8.33 trips
O
A
D
B
Expected travel time 27.75 min
Line
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
15 min
4 min
O
A
D
B
E6 min
10 min
New walk path is 26 min
12 min 12 min 30 min 6 min 10 min
HeadwayLine
6 min
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
15 min
4 min
O
A
D
B
E
10 min
First strategy time is 27.75 min
12 min 12 min 30 min 6 min 10 min
HeadwayLine
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
15 min
4 min
O
A
D
B
E6 min
10 min
Second strategy time is 26.00 min
12 min 12 min 30 min 6 min 10 min
HeadwayLine
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
15 min
4 min
O
A
D
B
E6 min
10 min
New walk path is 26 min (vs 27.75 min)Optimal strategy is to walk to the orange line
12 min 12 min 30 min 6 min 10 min
HeadwayLine
Logit Choice of Strategies
12 min12 min30 min 6 min10 min
Headway22.9 trips
22.9 trips
54.2 trips
19.08 trips
O
A
D
B
Line
E
3.82 trips
TRB Applications Conference Reno 2011
Logit choice of strategies (with scale = 0.1)First strategy 45.8 tripsSecond strategy 54.2 trips
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
17 min
4 min
O
A
D
B
E6 min
10 min
The travel time of the orange line is increased by 2 minutes to 17 minutes
12 min 12 min 30 min 6 min 10 min
HeadwayLine
TRB Applications Conference Reno 2011
Logit Choice of Strategies
4 min
7 min
25 minutes
6 min
17 min
4 min
O
A
D
B
E6 min
10 min
Second strategy time is now 28.00 min
12 min 12 min 30 min 6 min 10 min
HeadwayLine
TRB Applications Conference Reno 2011
Adding a Walk-to-transit Option
4 min
7 min
25 minutes
6 min
17 min
4 min
O
A
D
B
E6 min
10 min
New walk path is 28 min vs 27.75 minOptimal strategy does not use the walk to the orange line
12 min 12 min 30 min 6 min 10 min
HeadwayLine
TRB Applications Conference Reno 2011
Logit Choice of Strategies
O
A
D
B
E
12 min 12 min 30 min 6 min 10 min
HeadwayLine
Logit choice of strategies (with scale = 0.1)First strategy 45.8 50.6 tripsSecond strategy 54.2 49.4 trips
25.3 trips
25.3 trips
49.4 trips
21.1 trips
4.2 trips
TRB Applications Conference Reno 2011
Motivation Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions
Contents
TRB Applications Conference Reno 2011
Option 1Generate a set of paths by O-D pair prior to the execution of the route choice algorithmDrawbacks
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
How Can One Enlarge the Choice Set?
TRB Applications Conference Reno 2011
Option 2Enlarge the set of walk links and transit line segments that are considered in the transit assignment by using a well defined criterionAdvantage
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
How Can One Enlarge the Choice Set?
TRB Applications Conference Reno 2011
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.
Modified Strategy Computation
TRB Applications Conference Reno 2011
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
Modified Strategy Computation
Another Example
TRB Applications Conference Reno 2011
The demand is 100 in each direction
TRB Applications Conference Reno 2011
Another Example: Optimal Strategy
TRB Applications Conference Reno 2011
Scale: 0.2
Logit Choice of Strategies
TRB Applications Conference Reno 2011
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
Distribution of Flow Between Connectors
TRB Applications Conference Reno 2011
Scale: 0.2 Cut-off: 0.01
Logit Choice Only on Connectors
TRB Applications Conference Reno 2011
Another Example: Optimal Strategy
TRB Applications Conference Reno 2011
Optimal strategy when eastbound tram time is increased
Distribution of Flow – Increased Tram Time
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Logit on strategies when tram ride time is increased
Distribution of Flow – Increased Tram Time
TRB Applications Conference Reno 2011
Logit choice only on connectors
Distribution of Flow – Increased Tram Time
TRB Applications Conference Reno 2011
The issues that are addressed Computing logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions
Contents
TRB Applications Conference Reno 2011
Optimal strategy assignment:the flow at a transit node is distributed based on
frequencypl = 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 where the adjustment factor is computed as and the fastest line is considered first
Distribution of Flow Between Attractive Lines
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TRB Applications Conference Reno 2011
Optimal Strategy
Distribution of Flow Between Attractive Lines
TRB Applications Conference Reno 2011
Logit choice of strategies and transit time to destination
Distribution of Flow Between Attractive Lines
TRB Applications Conference Reno 2011
Motivation Logit choice of strategies Distribution of flow between connectors Distribution of flow between attractive lines Conclusions
Contents
TRB Applications Conference Reno 2011
The consideration of a richer set of strategiesInclusion of walk in “sub-optimal” strategiesModeling of uneven population distribution in large zonesEvaluation measures based on log-sum computationsWithout losing any computational efficiency…
Enhanced modeling possibilities