We consider aMX/G/1 queueing system withN-policy. The server is turned off as soon as the system empties. When the queue length reaches or exceeds a predetermined valueN (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 thePGF of the stationary system size of theMX/G/1 queueing system withoutN-policy and the other one has the probability generating function ∑j=0N=1 πjzj/∑j=0N=1 πj, in which πj is the probability that the system state stays atj before reaching or exceedingN during an idle period. Using this interpretation of the system size distribution, we determine the optimal thresholdN under a linear cost structure.
['Ho Woo Lee', 'Soon Seok Lee', 'Kyung-Chul Chae']
Operating characteristics of MX/G/1 queue with N-policy