Modeling and uncovering the passenger–taxi dynamic queues at taxi station with multiple boarding points using a Markovian environment

Abstract

The arriving of passengers at transport hubs often has a highly variable demand within a day; it makes the waiting times of both passengers and taxis unpredictable at taxi station of transport hubs. Aiming to uncover the queue dynamics of passengers and taxis at taxi station with multiple boarding points, this paper proposes a passenger–taxi matching queueing model by incorporating much more realistic descriptions including the number of boarding points, matching time, and variable arrivals over time, etc. In this paper, the passengers and taxis related queueing indices are derived, such as the overall average numbers of queueing passengers and taxis, the overall average waiting times of passengers and taxis, etc. In particular, the highly fluctuating queues of passengers and taxis at taxi station are respectively formulated by introducing the indices of conditional average numbers of both the queueing passengers and taxis at a given time. We also conduct a series of numerical experiments; the quantitative results will help us to understand the high variability of passengers’ and taxis’ queues at taxi station due to the variable arrival of passengers over time within a day. The obtained indices in this paper can provide an effective tool to evaluate the service level of passenger–taxi system, and thus contribute to improve the service of the passenger–taxi system at transport hubs according to the airport (or train, coach) schedule, weather, and traffic condition, etc.