On a single server queue with negative arrivals and request repeated

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.