Optimal incentive-compatible priority pricing for the M/M/1 queue
Operations Research
Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
Retrial queues with server subject to breakdown and repairs
Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
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In this paper, we examine the zero capacity M/M/1 queue with returning customers. Asymptotic bounds for the optimal state dependent retrial rate are derived, where the state of the process is determined by queue length and server status. This optimal return rate minimizes the penalty cost to a customer for waiting and checking in to verify that the server is busy. It will be shown that the problem reduces to three cases characterized by a linear relationship between four system parameters: customer arrival rate, service rate, competing retrial rate, and cost. In two of these cases, asymptotic bounds are tight.