On a batch matching system with impatient servers and boundedly rational customers

摘要

In this paper we consider a batch matching system with impatient servers and boundedly rational customers, which is essentially a double-ended batch service system. Each server is responsible for a batch of customers and serves them instantaneously. Especially, we assume that the servers have the characteristic of ”impatience”, which will lead to incomplete batch processing of each service. To derive the stationary distribution of system states, we combine two methods (called probability generating function method and G-matrix method), and some main performance measures are captured. In addition, we assume the customers are boundedly rational, that is, they are unable to estimate their sojourn times and utilities accurately. To deal, a logit model is employed to model this characteristic of the customers, and by which, we obtain the customers’ equilibrium joining fraction which is compared with the equilibrium joining probability of fully rational customers afterwards. Depending on whether the service is visible or invisible, we conduct some numerical analyses to show main parameters’ impact on equilibrium fraction, along with some intuitive explanations. Finally, to make the system viable economically, a function of service provider’s utility is developed and several numerical plots are presented to study the impact of several main parameters on the utility. Through the PSO (Particle Swarm Optimization) algorithm, we numerically obtain the maximum utility point within a certain range of multiple parameters.