A NEW LOOK ON THE SHORTEST QUEUE SYSTEM WITH JOCKEYING

Abstract

Abstract We introduce a Markov queueing system with Poisson arrivals, exponential services, and jockeying between two parallel and equivalent servers. An arriving customer admits to the shortest line. Every transition, of only the last customer in line, from the longer line to the shorter line may accompanied by a certain fixed cost. Thus, a transition from the longer queue to the shorter queue occurs whenever the difference between the lines reaches a certain discrete threshold (d = 2, 3, …). In this study, we focus on the stochastic analysis of the number of transitions of an arbitrary customer.