On the use of a fundamental identity in the theory of semi-Markov queues

Elja Arjas

41 citations0/0 files storedAdvances in Applied Probability

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

Abstract

In the paper a single server semi-Markov queue is considered. The analysis is based on a fundamental matrix identity due to H. D. Miller. A natural method for the solution of semi-Markov queues is indicated; use is also made of a duality relation, which is discussed in the paper.

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References

1962The stability of a queue with non-independent inter-arrival and service times 1967QUEUES AND INVENTORIES 1966Queues and Inventories.1966On the algebra of queues 1966The single server queue with Poisson input and semi-Markov service times 1967Queues with semi-Markovian arrivals 1967Time dependence of queues with semi-Markovian services 1962Stationary Waiting-Time Distributions for Single-Server Queues

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2006Fundamental characteristics of queues with fluctuating load 1975Random Flow in Queueing Networks: A Review and Critique 1986The single server semi-markov queue 2002An approximation for performance evaluation of stationary single server queues 1976On fluctuation problems in the theory of queues

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