On the use of a fundamental identity in the theory of semi-Markov queues
- 1 April 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 4 (02), 271-284
- https://doi.org/10.1017/s0001867800038350
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.Keywords
This publication has 17 references indexed in Scilit:
- Some Duality Results in the Theory of QueuesJournal of Applied Probability, 1969
- Markov renewal theoryAdvances in Applied Probability, 1969
- Queues with semi-Markovian arrivalsJournal of Applied Probability, 1967
- Boundary Problems for Sums of Lattice Random Variables, Defined on a Finite Regular Markov ChainTheory of Probability and Its Applications, 1967
- On the algebra of queuesJournal of Applied Probability, 1966
- The single server queue with Poisson input and semi-Markov service timesJournal of Applied Probability, 1966
- Stationary Waiting-Time Distributions for Single-Server QueuesThe Annals of Mathematical Statistics, 1962
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962
- Absorption Probabilities for Sums of Random Variables Defined on a Finite Markov ChainMathematical Proceedings of the Cambridge Philosophical Society, 1962
- A Convexity Property in the Theory of Random Variables Defined on a Finite Markov ChainThe Annals of Mathematical Statistics, 1961