Abstract
The formula for the blocking probability for the finite capacity M/G/1/K in terms of the steady state occupancy probability distribution of M/G/1 and the system utilization is known [Keilson, J. Royal Statistical Soc. Serie B, 28 (1966) 190–201]. The validity of this relationship is demonstrated for a broad class of state dependent M/G/1 vacation systems and priority systems. New methods are employed which may also be of interest in their own right.
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This research was conducted while J. Keilson was a Senior Staff Scientist at GTE Laboratories Incorporated.
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Keilson, J., Servi, L.D. The M/G/1/K blocking formula and its generalizations to state-dependent vacation systems and priority systems. Queueing Syst 14, 111–123 (1993). https://doi.org/10.1007/BF01153529
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DOI: https://doi.org/10.1007/BF01153529