Bounds for the mean system size in M/G/1/K-queues

Bounds for the mean system size in M/G/1/K-queues

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Article ID: iaor19961461
Country: Netherlands
Volume: 64
Issue: 1/2
Start Page Number: 149
End Page Number: 161
Publication Date: Nov 1995
Journal: Journal of Computational and Applied Mathematics
Authors: ,
Abstract:

Contrary to their infinite capacity counterparts, the moments of the distribution of the number in a M/G/1/K-system cannot be determined by means of the Pollaczek-Khinchine equation. If the finite capacity K is small the distribution under study can be obtained as the steady-state probability distribution related to the transition probability matrix. For larger capacities, the authors derive upper and lower bounds on the mean system size in an M/G/1/K-queue for which the first two moments of the number in the system of the infinite capacity queue are known. Numerical examples for the M/D/1/1-and M/D/1/3-queues are given.

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