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 assignment models are based on the classical assumption that at a given stop passengers board the first arriving carrier of a certain subset of the available lines, often referred to as the attractive set. In this case, it has been shown that, if the headway distributions are exponential, then an optimal subset of lines minimizing the passenger travel time can be easily determined. However, when online information on future arrivals of buses are posted at the stop, it is unlikely that the above classical assumption holds. In this case, passengers may choose to board a line that offers the best combination of displayed waiting time and expected travel time to their destination once boarded. In this paper, we propose a general framework for determining the probability of boarding each line available at a stop when online information on bus waiting times is provided to passengers. We will also show that the classical model without online information may be interpreted as a particular instance of the proposed framework, this way achieving an extension to general headway distributions. The impact of the availability of information regarding bus arrivals and that of the regularity of transit lines on the network loads, as well as on the passenger travel times, will be illustrated with small numerical examples.
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