Operating characteristics of M(x)/G/1 queue with N-policy

Abstract

We consider a MX/G/1 queueing system with N-policy. The server is turned off as soon as the system empties. When the queue length reaches or exceeds a predetermined value N (threshold), the server is turned on and begins to serve the customers. We place our emphasis on understanding the operational characteristics of the queueing system. One of our Findings is that the system size is the sum of two independent random variables: one has tile PGF of the stationary system size of the MX/G/1 queueing system without N-policy and the other one has the probability generating function ~o 17rjzY/~-o I rcj, in which 7rj is the probability that the system state stays atj before reaching or exceeding N during an idle period. Using this interpretation of the system size distribution, we determine the optimal threshold N under a linear cost structure.