Modeling the dynamical behavior of the passenger-taxi queue matching problem at traffic hubs

Taxis are one of the most important modes of transport in major passenger traffic hubs. Due to the inherent unpredictability of passenger arrivals and their strong correlation with passenger arrival times, it often results in excessively long passenger queues if a large number of passengers arrive suddenly, or excessively long taxi queues at the other end if a few passengers arrive during the non-burst period at the taxi stand in the traffic hubs. In particular, when a sudden arrival of a large number of passengers fails to evacuate in a short period of time, followed by another burst in passenger arrivals, the service performance of the system deteriorates dramatically. In order to quantitatively analyze the dynamical queueing behavior of the passenger-taxi matching problem at transport hubs against the background of many uncertain factors, we propose a double-input matching model based on queueing theory, which covers basic practical elements, including time-varying arrivals of passengers and taxis, a randomly matched number of passengers, a random matching time, and multiple waiting queues. We determine the steady-state condition of the system, derive the steady-state queue length probability distributions of passengers and taxis, and further obtain the overall average queueing performance metrics of passengers and taxis and the dynamic queueing metrics over time. Numerical simulations examine the impact of the stochastic arrival process of passengers over a long period of time on the dynamical performance metrics of the system. In particular, for continuous and discontinuous bursty arrivals of passengers over a period of time, we clarify how the long queues caused by bursty arrivals of passengers dissipate at subsequent times and also examine the impact of variations in passenger arrival rates during a specific time period on queueing performance throughout the system.