Transient solution of an M/M/1 queue with catastrophes

A note on birth–death processes with catastrophes

“…Markov chains subject to catastrophes (see , Economou and Fakinos, 2003, Kyriakidis, 2001, 2002, Pakes, 1997, Stirzaker, 2001, Swift, 2000, and Switkes, 2004; (vi) analysis of the effect of catastrophes and jumps in the case of M/M/1 and other Markov queueing systems (see Chen and Renshaw, 1997, and Di Crescenzo et al, 2003, including the case when the number of initially present customers is random (see Krishna Kumar and Arivudainambi, 2000). Two recent papers are also of interest : Stirzaker (2006) looks at hitting times for a general Markov processes subject to catastrophes, whereas Stirzaker (2007) deals with an even more general model where the process is switched to another state at Poisson event times, and the change of state is governed by a stochastic matrix.…”

Continuous-time random walks with reset events

“…Almost two decades later, in 1994, Kyriakidis [7] studied a more concrete application of these techniques in a population birth-death process with immigration and stochastic total catastrophes. Since then, a variety of different discrete Markov processes with resets have been proposed to model systems as, e.g., populations [8,9] or queues [10,11] -both in the discrete and continuous limit.…”

Reliability Analysis of a Two-Server Heterogeneous Unreliable Queueing System with a Threshold Control Policy

“…A queueing system with two heterogeneous servers and multiple vacations was studied by Kumar and Madheswari [6], who obtained the stationary queue length distribution by using matrix geometric method and provided analysis of busy period and waiting time. In Kumar et al [7] the same authors have introduced the M/M/2 queueing system with heterogeneous servers subject to catastrophes and provided a transient solution for the system under study. A heterogeneous two-server queueing system with balking and server breakdowns has been studied by Yue et al [16].…”