Route choice on transit networks with on-line information at stops

Passengers on a transit network with common lines are often faced with the problem of choosing between either to board the arriving bus or to wait for a faster one. Many existing assignment models are based on the classical assumption that at a given stop passengers board the first arriving carrier of a certain subset of available lines. It has been shown that, in this case, an {\it optimal subset} of lines that minimizes the passenger travel times exists and is easily determined if the headway distributions are exponential. However, when on-line information on future arrivals of buses are posted at various stops, it is unlikely that the above classical assumption holds. Passengers may choose in this case to board a line that offers the best combination of waiting time and expected remaining time. We propose in this paper a general framework for determining the probability of boarding each available line at a stop when on-line information on bus arrivals is provided to passengers. We will also show that the classical case without on-line information may be interpreted as a particular instance of the proposed framework, and thus extend the results obtained with exponential distributions to generaldistributions. Numerical examples, based on various headway distributions proposed in the literature, will be used to illustrate the combined impacts of the regularity of transit lines and of the availability of information regarding bus arrivals at stops on the line loads and on the passenger travel times