On a finite-buffer bulk-service queue with disasters

Abstract

We deal with a finite-buffer bulk-service queue with disasters. The arrival streams of units and disasters are Markovian arrival processes (MAPs). We study the stationary distribution of the embedded Markov chain at post-departure epochs. The block structure allows us to derive a general approach amenable to numerical calculation following results of the theory for censored Markov chains and level-dependent quasi-birth-and-death processes. We give tractable analytical formulas for the departure process and the stationary distributions of the system state at arbitrary and pre-arrival epochs. The effect of the disaster stream on certain probabilistic descriptors is graphically illustrated.