On the M/G/1 Queue with Rest Periods and Certain Service-Independent Queueing Disciplines

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Abstract
The M/G/1 queue with rest periods and FCFS order of service was first studied by Miller. We give further results concerning the behavior of the delay under the FCFS discipline. We then solve for the second moment of the waiting time in an M/G/1 queue with rest periods and Random Order of Service (ROS). We finally solve for the Laplace-Stieltjes transform of the distribution function of the waiting time in an M/G/1 queue with rest periods and nonpreemptive LCFS order of service. The relationship found between the second moments of the waiting time in an M/G/1 queue with rest periods under the FCFS, ROS and LCFS disciplines is precisely that found by Takács for the M/G/1 queue without rest periods.