Analysis of Repairable Geo/G/1 Queues with Negative Customers

Abstract

We consider discrete-time Geo/G/1 queues with negative customers and a repairable server. The server is subject to failure due to a negative customer arrival. As soon as a negative customer arrives at a system, the server fails and one positive (ordinary) customer is forced to leave. At a failure instant, the server is turned off and the repair process immediately begins. We construct the mathematical model and present the probability generating functions of the system size distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given to show the influence of negative customer arrival on the performance measures of the system.