Throughput analysis of a two station closed queueing network with blocking and server breakdown

Abstract

An exact analysis is presented to compute the throughput of a two station closed queueing network with multiple servers subject to blocking and breakdown of servers. Blocking occurs in a network when a job after completing service at station i and wanting to enter station j is forced to remain at station i, thus blocking station i, until room is available at station j. This type of blocking is known as classical blocking. One of the stations with multiple servers is subject to a breakdown of one of the servers. This means that the station subject to failures alternates between two modes of operation. In one mode all the s servers are available and in the other mode only (s — 1) servers are available. We first show that for a two station closed queueing network with blocking and server breakdown (at one of the stations), there exists an equivalent non-blocking two station closed queueing network with only server break-down. This is due to the fact that both the networks have the same state space structure....