Optimal strategy analysis of an N-Policy M[X]/M/1 queueing system with a removable and non-reliable server

This paper analyses the modeling of a production system, which is designed as an N-policy M^[X]/M/1 queueing system with a removable and non-reliable server. The server spends a random period for startup procedure before each new service. The server does not start the production until some specified number of raw materials ‘N’ are accumulated in the queue and it stays idle when there is no input unit to process. The server is susceptible for random breakdown and in such a case it is repaired at once and it resumes the service. The units are assumed to arrive in batches of random size. Various system measures and stochastic decomposition property are obtained using generating functions. Optimal operating policy is achieved under a linear cost structure and a sensitivity analysis is presented through numerical illustrations.