MARKOVIAN QUEUE WITH N-SERVERS SUBJECT TO BREAKDOWNS AND REPAIRS

A study is made of a queue with N servers, who may break down and require repair at a facility, which has c repair crews. Under exponential assumptions, this model has an algorithmically tractable solution. It is then in fact a particular case of the M/M/N queue in a Markovian environment. By numerical examples, it is shown that during periods when most servers are down, large build-ups may occur whch affect the queue adversely for a long time afterward. Authors also find that such build-ups are aggravated by reducing the number of repair crews, but may be attenuated by reducing the arrival rates during periods when the service has deteriorated. This work is pertinent to maintenance.