A Matrix Analytic Solution of a Finite Buffer Queue with PH Distributed Customers ’ Impatience ⋆

Abstract. We study a multiserver finite buffer queue in which customers have a stochastic deadline of phase-type until the beginning of their service. The following service disciplines are considered: FCFS (First-Come First-Served), LCFS (Last-Come First-Served) and SIRO (Service In Random Order) along with a parameterizable probabilistic pushout mechanism. The analysis of the system is performed using a matrix analytic approach and we obtain performance measures such as probabilities of blocking, expulsion and abandonment as well as the sojourn time distribution in different system conditions