Numerical Analysis of Retrial Queueing Systems with Conflict of Customers and an Unreliable Server

Abstract

In this paper a closed retrial queueing system is considered with a finite number of customers. If an arriving (primary or secondary) request finds the server busy, two modes are possible: the job is transferred to the orbit (no conflict) or the job under service is interrupted and both of them are transferred to the orbit (conflict). Jobs in the orbit can retry reaching the server after a random time. The unreliable case where the server is subject to breakdown is also investigated. These types of systems can be solved by numerical, asymptotical, and simulation methods. The novelty of the investigations is that it provides a new approach to an algorithmic solution for calculating the steady-state probabilities of the system. With the help of these probabilities the main performance measures can be computed. Several sample examples illustrate the effect of different parameters on the distribution on requests in the system.