A NEW LOOK ON THE SHORTEST QUEUE SYSTEM WITH JOCKEYING

We introduce a service system with Poisson arrival, exponential services and jockeying between two of parallel and equivalent servers. An arriving customer admits to the shortest line (when the lines are equal the customer admits to any line with probability 0.5). Every transition, of only the last customer in line, from the longer line to the shorter one is 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.