Priorities at the end of service

Abstract.: Consider a (Formula presented.) queue with N customer priority classes, all with the same service requirement distribution. The special feature of the model is that the assignment of a job is done at the end of the service period–it is assigned to a customer of the highest priority class then present. Two variations of this scheme are studied: (i) the stoppable server case, in which the server only works when there are customers, and (ii) the unstoppable case, in which the server always works but scraps a job when at its completion there is no customer to receive it. For both variants, we determine the probability generating function of the steady-state joint queue length distribution, as well as the Laplace-Stieltjes transform of the sojourn time distribution of each class. This is done in detail for N = 2 customer classes and more globally for general N.