Analysis of the Exceptional Queueing System by the Use of Regenerative Processes and Analytical Methods

Do Le Minh

19 citations0/0 files storedMathematics of Operations Research

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

This paper studies a queueing system in which the distributions of the first inter-arrival time and the first service time of each busy period are allowed to deviate from the usual GI/G/1 pattern. Under conditions insuring stability, we use analytical methods together with the property that the queueing process “starts anew” probabilistically whenever an arriving customer initiates a busy period to obtain various transient and stationary results for the system.

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References

1983The Single Server Queue.1964On a Generalized M/G/1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service 1953On the distribution of queueing times 1976On Regenerative Processes in Queueing Theory 1974Simulating Stable Stochastic Systems, I: General Multiserver Queues 1972Regenerative processes in the theory of queues, with applications to the alternating-priority queue 1966On the algebra of queues 1962Single server queues with modified service mechanisms

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1989Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and applications

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