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Buffer overflow calculations using an infinite-capacity model

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  • Schweitzer, Paul J.
  • Konheim, Alan G.

Abstract

Sufficient conditions are established for approximation of the overflow probability in a stochastic service system with capacity C by the probability that the related infinite-capacity system has C customers. These conditions are that (a) the infinite-capacity system has negligible probability of C or more customers; (b) the probabilities of states with exactly C customers for the infinite-capacity system are nearly proportional to the same probabilities for the finite- capacity system. Condition (b) is controlling if the probabilities for the infinite-capacity system are rescaled so that the probability of at most C customers is unity. For systems with precisely one state with C customers, such as birth-and-death processes, the latter approximation is exact even when condition (a) does not hold.

Suggested Citation

  • Schweitzer, Paul J. & Konheim, Alan G., 1978. "Buffer overflow calculations using an infinite-capacity model," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 267-276, February.
    • Handle: RePEc:eee:spapps:v:6:y:1978:i:3:p:267-276
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    Cited by:

    1. Tijms, H.C., 1991. "A new heuristic for the overflow probability in finite-buffer queues," Serie Research Memoranda 0029, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Smith, J. MacGregor & Cruz, F.R.B. & van Woensel, T., 2010. "Topological network design of general, finite, multi-server queueing networks," European Journal of Operational Research, Elsevier, vol. 201(2), pages 427-441, March.

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