Sang Nguyen, Université de Montréal
Modeling passengers assignment on transit networks
On a transit network, a passenger who boards a carrier and finds a seat can keep it until he gets off the carrier. This seemingly innocuous first come - first served rule significantly enhances the difficulty of modeling the passengers assignment on a transit network, where arriers have rigid capacities, as an equilibrium multicommodity flow problem. Two distinct modeling approaches, a path flow based on the notion of available capacity and a strategic flow with loading priorities, giving rise to different variational inequality formulations will bediscussed. Both theoretical and computational insights will be presented.
Paolo Ferrari, Università di Pisa
Road pricing, public transport and users' welfare
Guido Gentile, Università di Roma "La Sapienza"
Rethinking the wait model at transit stops
Consider a transit network with common lines in which passengers' behavior is based on line frequencies, instead of their timetables. The classical assumption is that the passenger will board the first arriving carrier among the lines which are perceived to be attractive. In almost all the models proposed in the literature and widely adopted to plan transit systems the attractive set has been considered static, e.g., it is not modified during the wait. This approach is not consistent with the rational behavior assumption. Indeed, passengers decide whether it is convenient to board an arriving carrier rather than to pursue waiting for a better subsequent arrival, taking into account the time already waited at the stop. So, a line can be attractive at a given waited time, and not necessarily for the entire waiting process, yielding a dynamic attractive set model. The static approach is valid only when the headway distribution of all the lines is exponential, since in this case there is actually no temporal evolution of the attractive set; though the exponential distribution is quite unrealistic. Moreover, when on-line information on future arrivals of buses are posted at a stop, passengers may choose to board a line that offers the best combination of displayed time and expected travel time to destination once boarded. We propose in this paper a general framework for determining the probability of boarding each available line at a stop and the corresponding expected waiting and travel times, with and without on-line information.