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]

Overview

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". Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064). Vol. 2. pp. 631–640. 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.
Stub icon

This probability-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.