Optimization in a passenger-taxi service system with different arrival rates of taxis based on a double-ended Markovian queue

In order to improve the efficiency of comprehensive transportation hubs, we study the optimization in the passenger-taxi service system with different arrival rates of taxis based on a double-ended queue. The objective to maximize the social benefit (sum of a passenger and a taxi benefits) with the strategic behavior of passengers who decide whether to join the system or balk in the observable case and the unobservable case. By the theory of Markov chain and the double-ended queueing system, we obtain the waiting times of a passenger and a taxi, respectively. Combined with the reward-cost structure, we get the social benefit functions in two cases. Then, we investigate the social benefit functions by some numerical examples. We study the optimization of the social benefit functions in two cases for several parameters, such as the low arrival rate of taxis, the arrival rate of passengers, and the taxi buffer size. In general, the social benefit in the observable case is more than that in the unobservable case. The managers in comprehensive transportation hubs can improve the social benefit by establishing an information platform, optimizing the arrival rate of taxis, leading the choice of passengers and setting the optimal taxi buffer size.