Stationary analysis of a fluid queue driven by an M/M/1/N queue with disaster and subsequent repair

Abstract

This paper studies a fluid queueing model driven by an M/M/1/N queue subject to disaster and subsequent repair. The underlying system of differential difference equations that governs the process are solved using generating function methodology. Explicit expressions for the joint steady state probabilities of the state of the background queueing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind. Numerical illustrations are added to support the theoretical results.