The <i>T</i>-Policy for the <i>M</i>/<i>G</i>/1 Queue

We consider situations where the server cannot continuously monitor its queue to sense customer arrivals. For this situation we introduce the T-policy which activates the server T time units after the end of the last busy period. We consider in detail an M/G/1 queue with linear customer holding costs and a fixed charge for activating the server. For the minimum cost-rate criterion we obtain the optimal value of T and the optimal cost rate. We show that the optimal cost rate is larger than the one achieved by the comparable optimal N-policy which activates the server when N customers are in the queue. We also show that under the optimal T-policy, the expected number of customers present when the server is activated is the optimal value of N.

• 저널Management Science · 23(7) · 775–778
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.23.7.775
• 저자Daniel P. Heyman