Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue
- 1 March 1994
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 31 (01) , 235-243
- https://doi.org/10.1017/s0021900200107478
Abstract
By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in theMAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for theMAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.Keywords
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