A Markovian analysis of the finite-buffer M/D/1 queue

The paper presents a new method for analysing the performance of the finite-buffer M D 1 queueing system. The basis of the method is to formulate the system as a piecewise-deterministic Markov process (PDP) and then to compute the required performance characteristics using suitably tailored versions...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 1997-09, Vol.453 (1964), p.1947-1962
Main Authors: Davis, M. H. A., Howl, J. M.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Cemeteries
Curves
Markov models
Markov processes
Ordinary differential equations
Spacetime
Sufficient conditions
Vector fields
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Summary:The paper presents a new method for analysing the performance of the finite-buffer M D 1 queueing system. The basis of the method is to formulate the system as a piecewise-deterministic Markov process (PDP) and then to compute the required performance characteristics using suitably tailored versions of certain results from general PDP theory. This approach yields explicit formulae for important performance parameters such as equilibrium mean queue length and buffer saturation probability. It also leads to an effective numerical algorithm for computing non-equilibrium behaviour.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.1997.0105