The optimal planning computerized manufacturing systems

The utility of interactive computation in answering questions on the behavior, design, and control of certain service systems is demonstrated. The stationary distributions of various waiting times are also discussed. A queue with N servers which may break down and require repair at a facility which has C repair crews is studied. Under exponential assumptions, this model has an algorithmically tractable solution. It is then a particular case of the M/M/n queue in a Markovian environment. It is shown that during periods when most servers are down, large build-ups may occur which affect the queue adversely for a long time afterwards. Potential applications are in manpower planning, as in a typing pool where persons may be absent, and in determining the size of a battery of machines, where machines may be inoperative due to maintenance and repair.