Sojourn times in a two-stage queueing network with blocking

Abstract

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines. The main feature of our model is blocking, i.e., as soon as the second waiting line reaches a certain upper limit, the first line is blocked. The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type. Our objective is to study the sojourn time distribution under the first-come-first-serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi-birth-and-death processes and continuous-time Markov chains.