Sojourn Time Analysis for Processor Sharing Loss System with Unreliable Server

Abstract

Processor sharing (PS) queuing systems and particularly their well-known class of egalitarian processor (EPS) sharing are widely investigated by research community and applied for the analysis of wire and wireless communication systems and networks. The same can be said for queuing systems in random environment, with unreliable servers, interruptions, pre-emption mechanisms. Nevertheless, only few works focus on queues with both PS discipline and unreliable servers. In the paper, compared with the previous results we analyse a finite capacity PS queuing system with unreliable server and an upper limit of the number of customers it serves simultaneously. For calculating the mean sojourn time, unlike a popular but computational complex technique of inverse Laplace transform we use an effective method based on embedded Markov chains. The paper also includes a practical numerical example of web browsing in a wireless network when the corresponding low priority traffic can be interrupted by more priority applications.