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Explicit Formulae for Characteristics of Finite-Capacity M/D/1 Queues

  • Seo, Dong-Won (Kyung Hee School of Management and also with the Management Research Institute, Kyung Hee University)
  • Received : 2013.08.19
  • Accepted : 2013.11.08
  • Published : 2014.08.01
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Abstract

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transform-free) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ${\rho}$, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector $D_n$ are available.

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References

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