Choice Models in Frequency-based Transit Assignment

Choice Models in Frequency-based Transit Assignment


K Noekel, S Wekeck, PTV AG, DE


The paper compares the Optimal Strategies model for frequency-based assignment and two alternative models. Probabilistic strategies improve passenger utility still further. Also continuity in route choice improves convergence of demand models.


Frequency-based transit assignment aims to model the choices of transit passengers who select their itinerary based on their knowledge of routes, travel times and frequencies (or headways) of the lines in the network. The existing approaches can be classified according to the assumptions they make about
? Regularity of service (distribution of inter-arrival times for each line),
? Arrival distribution of passengers at stops,
? Capacity constraints,
? Information available to passengers,
? the structure of the choice set considered by each passenger.
The majority of existing approaches adopt the Optimal Strategies framework developed by Spiess and Florian (1989) and Nguyen and Pallottino (1988) and assume stochastically independent and exponentially distributed inter-arrival times and uniformly distributed passenger arrivals. Passengers observe only the next line to be served at a transfer stop. For the uncongested case, it was shown that under these conditions a passenger will minimise total estimated travel time by adopting a hyperpath strategy. A hyperpath prescribes for each boarding stop a set of attractive lines (each with an alighting stop). The traveller executes a hyperpath strategy by boarding the first arriving vehicle from any line in the attractive set of the origin stop, riding it until the alighting stop, and repeating the procedure there until the destination is reached.

However, the assumptions underlying the Optimal Strategies model may not always be justified in reality. In particular, the assumption of exponentially-distributed inter-arrival times simplifies the mathematical treatment, yet is a poor model of reality, if services actually run with higher regularity. Ultimately, in these cases passengers may behave as assumed in timetable-based assignment, but there are decision situations where a frequency-based approach may still mirror actual traveller behaviour better. In the paper we revisit two such situations of practical relevance which have been proposed before by Billi, Gentile, Nguyen, Pallottino (2004) and by Gentile, Nguyen, Pallottino (2003).

The paper compares all three route choice models and contributes two additional results. Firstly, it is shown that the common approach of a deterministic choice set can significantly be improved by applying a probabilistic strategy. Depending on the elapsed wait time observed, passengers pick an arriving vehicle with a certain probability, thereby minimizing their expected generalized cost. Secondly, all of these alternative route choice models, in addition to capturing traveller behavior more realistically, share a very desirable property: as running times or headways vary continuously, so do the line shares. In contrast, small changes may lead to large discontinuities in the original model. These step changes may adversely affect convergence of travel demand models with feed-back, where e.g. small mode-shifts lead to changes in car travel time, and transit running times are updated based on these.


Carolina Billi, Guido Gentile, Sang Nguyen, Stefano Pallottino (2004): Rethinking the wait model at transit stops, Proc. TRISTAN-Workshop, Guadelupe, 2004

Guido Gentile, Sang Nguyen, Stefano Pallottino (2003): Route choice on transit networks with on-line information at stops, Technical Report TR-03-14, University Roma 1 ?La Sapienza?

Sang Nguyen, Stefano Pallottino (1988): Equilibrium traffic assignment for large scale transit networks, European Journal of Operational Research 37(2), 176-186.

Heinz Spiess, Michael Florian (1989): Optimal strategies: A new assignment model for transit networks, Transportation Research B 23(2), 83-102.


Association for European Transport