Beneš method

In queueing theory, a discipline within the mathematical theory of probability, Beneš approach[1] or Beneš method[2] is a result for an exact or good approximation to the probability distribution of queue length. It was introduced by Václav E. Beneš in 1963.[3]

The method introduces a quantity referred to as the "virtual waiting time" to define the remaining workload in the queue at any time. This process is a step function which jumps upward with new arrivals to the system and otherwise is linear with negative gradient.[4] By giving a relation for the distribution of unfinished work in terms of the excess work, the difference between arrivals and potential service capacity, it turns a time-dependent virtual waiting time problem into "an integral that, in principle, can be solved."[5]

References

  1. ^ Sivaraman, V.; Chiussi, F. (2000). Providing end-to-end statistical delay guarantees with earliest deadline first scheduling and per-hop traffic shaping. IEEE INFOCOM (Conference on Computer Communications). Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064). Proceedings IEEE INFOCOM 2000. Vol. 2. p. 631. doi:10.1109/INFCOM.2000.832237. ISBN 0-7803-5880-5.
  2. ^ Norros, I. (2000). "Queueing Behavior Under Fractional Brownian Traffic". Self-Similar Network Traffic and Performance Evaluation. pp. 101–114. doi:10.1002/047120644X.ch4. ISBN 0471319740.
  3. ^ Beneš, V. E. (1963). General Stochastic Processes in the Theory of Queues. Addison Wesley.
  4. ^ Reich, E. (1964). "Review: Vaclav E. Benes, General Stochastic Processes in the Theory of Queues". The Annals of Mathematical Statistics. 35 (2): 913–914. doi:10.1214/aoms/1177703602.
  5. ^ Van Mieghem, P. (2006). "General queueing theory". Performance Analysis of Communications Networks and Systems. pp. 247–270. doi:10.1017/CBO9780511616488.014. ISBN 9780511616488.


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