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

Article Abstract:

The M-G-I queue with rest periods and FCFS order of service was first studied by Miller. Further results concerning the behavior of the delay under the FCFS discipline are given. The second moments of the waiting time in an M-G-I queque with rest periods and random order of service (ROS) is then solved. Finally the Laplace-Stieltjes transform of the distribution function of the waiting time in an M-G-I queque with rest periods on nonpreemptive LCFS order of service is solved. The relationships found between the second moments of the waiting time in an M-G-I queue with rest periods under the FCFS, ROS and LCFS disciplines are precisely those found for the M-G-I queue without rest periods. A graph shows the time spent in the system including idle time. A second graph shows wait time by customers. A table of moments of the waiting time is also included.

Mathematical models, Applications, Models, Systems, Theory, Queues

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Diffusion Approximation for an M-G-m Queue

Article Abstract:

The M-G-m queueing system in the steady state is discussed. Applying the method of diffusion approximation, approximate formulas are provided for the distribution of the number of customers, the waiting time and the busy period. The relation between heavy traffic approximation and these approximations are discussed. In order to examine the accuracy of the approximate formulas, they are numerically tested on some examples.

Diffusion (Physics), Approximation, Queuing Networks, Diffusion

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A Note on Linearly Decreasing, Delay-Dependent Non-Preemptive Queue Disciplines

Article Abstract:

Linearly increasing, delay-dependent priority systems with exponential interarrival and service times are reviewed. Hsu extended the research by considering priorities that decrease linearly with time. Two errors in Hsu's paper are addressed. A graph illustrates the determination of priority.

Review, Scientific Research

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