Analysis of a random N-policy Geo/G/1 queue with the server subject to repairable breakdowns

Abstract This study investigates a random N-policy Geo/G/1 queue with the server subject to repairable breakdowns in which the threshold N is newly determined every regenerative cycle. When the system empties, the server stops services until the waiting customers attain the threshold value N. The important system characteristics such as the system length, idle period, busy period, breakdown period, and waiting time are derived. Some numerical examples show the influence of the critical system parameters on the cost function. We apply the probabilistic global search Lausanne algorithm to obtain the minimal cost in which the parameter of the threshold N distribution is decision variable. We also present an application example to demonstrate the applicability of investigated model.

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