Queueing system with server breakdowns and individual customer abandonment

Abstract

ABSTRACT We consider a single server queueing system with a finite capacity buffer in which the server is subject to breakdowns and repairs. At the time of a breakdown, the customers, if any, present in the system will either decide to stay or abandon according to a probabilistic mechanism. This decision is made by every customer present in the system independent of the others. We assume that the arrivals of customers occur according to a Markovian arrival process (MAP). The shocks that create breakdowns of the servers are also assumed to follow a MAP independent of the other MAP. The service and the repair times of the server are assumed to follow (possibly) different phase type (PH) distributions. An arriving customer finding the buffer full will be lost. Further, an arriving customer finding the server under repair may decide to balk or join the queue at that instant. This queueing system, which generalizes some of the well-known queueing models in the literature, is studied as a GI/ M/ 1- type with a finite state space. The model is analyzed in steady-state and illustrative numerical examples including an optimization problem of interest are presented.