Analysis of a Retrial Queueing System Suitable for Modeling Operation of Ride-Hailing Platforms with the Dynamic Service Pricing

Abstract

Effective operation of any service system requires optimal organization of the sharing of resources between the users (customers). To this end, it is necessary to elaborate on the mechanisms that allow for the mitigation of congestion, i.e., the accumulation of many users requiring service. Due to the randomness of the user’s arrival process, congestions can occur even when an arrival rate is constant, e.g., the arrivals are described by the stationary Poisson process, which is assumed in the majority of existing papers. However, congestions can be more severe if the possibility of fluctuation of the instantaneous arrival rate exists. Such a possibility is an inherent feature of many systems and can be taken into account via the description of arrivals by the Markov arrival process (MAP). This makes the problem of congestion avoidance drastically more challenging. In many real-world systems, there exists the possibility of customer admission control via dynamic pricing. We propose a novel predictive mechanism of dynamic pricing. Decision moments coincide with the transition moments of the underlying process of the MAP. A customer may join or balk the system or postpone joining the system depending on the current cost. We illustrate the application of this mechanism in a multi-server retrial queueing model with dynamic service pricing. The behavior of the system is described by a multidimensional Markov chain with state-inhomogeneous transitions. Its stationary distribution is computed and may be used for solving the various problems of system revenue maximization via the choice of the proper pricing strategy.