Matrix analytical methods for M/PH/1 Retrial queues

Jeffrey E. Diamond · Attahiru Sule Alfa

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

A matrix analytical approach is applied to retrial queues with phase type service time distributions. A matrix product form is obtained for the joint stationary distribution of queue length and service phase and a stability condition is derived. A numerical method is derived for obtaining the distribution of the number of retrials per customer and the distribution and moments of the waiting time in orbit. We also consider two extensions: The M/M/l retrial queue with geometric loss and state dependent M/PH/1 retrial queues

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References

1990A survey of retrial queues 1987A survey on retrial queues 1989A survey on retrial queues 1990Numerical investigation of a multiserver retrial model 1968A Service System with Unfilled Requests Repeated 1986A general class of Markov processes with explicit matrix-geometric solutions 1984A service model in which the server is required to search for customers 1990Matching moments to phase distributions: nonlinear programming approaches

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2014Mathematical Analysis of Queue with Phase Service: An Overview

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