N-PARALLEL QUEUING-SYSTEMS WITH SERVER BREAKDOWN AND REPAIR

A model is presented that can be used to study the influence of machin e breakdown and limited repair capacity on the performance of a system that has to provide service continuously. We consider a system consis ting of N stations, each serving its own stream of customers. The serv ers of the stations are subject to breakdown. Broken servers are repai red by a joint repair facility consisting of K parallel repairmen. Whe never K < N, this repair facility is causing interference between the N stations. We present both an exact (matrix-geometric) solution and a simple approximation (employing stochastic decompositions) of the dis tribution of the queue length at a particular station. With this model various design issues can be investigated such as the number of repai rmen that is needed to maintain a pool of machines, or the number of m achines that can be assigned to a certain crew of repairmen. Several n umerical examples illustrate the approach.