Due to recent applications in health care systems and in queues with impatient customers arising in telecommunication networks and inventory systems with perishable goods, there has been renewed interest in priorization of units in queueing models. In the literature on priority queues, a great number of probabilistic models possessing a variety of properties have been discussed. In general, most chapters in textbooks and papers on priority queues treat those with exogenous priority rules.
The aim of this work is to study self-generation of priorities in multi-server queues of finite capacity accomodating units that arrive from a Markovian arrival process (MAP) and require service times if phase (PH) type. The MAP is a wide generalization of the Poisson process and contains a great class of numerically tractable point processes as special cases. Section 2 is devoted to the finite capacity MAP/PH, PH/C/C+N queue with self-generation of priorities. In Section 3, the focus is on the continuous-time Markov chain at arbitrary times which represents a finite quasi-birth-and death process. An efficient computational approach to its analysis is derived. In Section 4 entitled “Performance evaluation” the authors give tractable analytical formulas for the departure process, the blocking probability, and the stationary distributions at pre-arrival epochs, at post-departure epochs and at epochs at which arriving units are lost. Finally, the effect of several parameters on probabilistic descriptors of our queue is graphically presented.