Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers

Abstract

In this paper, we consider a queueing system consisting of two multi-server subsystems that is designed for the service of clients arriving at a system according to a Markovian arrival process (MAP). Arriving clients receive information about the number of clients present in both subsystems and use this information to make a randomized decision to balk (depart without receiving service) or join the system. In the latter case, they also decide which subsystem they would like to join. One subsystem has an infinite buffer, while the buffer of the second subsystem is finite. The service time distribution is exponential in the first subsystem and phase-type in the second subsystem. During the waiting in the chosen buffers, after the random time intervals, each waiting client checks the status of the alternative subsystem. If some server in that subsystem is idle during this epoch, the client immediately leaves the buffer where it has been staying and starts a service in the alternative subsystem. The problem of computing the steady-state distribution of this system is solved. The feasibility of the proposed solution and certain features of the system’s behavior are numerically illustrated.