The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Approximations to blocking probability in two-stage queueing model

이단계 대기모형에서 손실확률에 대한 근사

  • Published : 1997.12.01
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Abstract

We ivestigate a two-stage queueing system which frequently arises in the study of overflow problems. A primary service facility consists of multiple primary queues where blocked calls are overflowed to a secondary queue. By approximating the input to the secondary queue with a two-state Markov Modulated Poisson Process (MMPP), we derive the blocking probability of the secondary queue. For the approximation, we employ the well-known Heffes' method and the SAM procedure.

본 논문에서는 오버플로우에 관한 연구에서 흔히 나타나는 이단계 대기모형을 연구하였다. 첫번째 단계는 여러개의 큐(queue)로 이루어져 있고, 이 큐들의 수용능력을 넘어서는 순간에 두번째 단계로 오버플로우가 발생한다. 두번째 단계로의 입력과정을 두 개의 상태를 가지는 MMPP로 근사함으로써 손실확률에 대한 계산을 이끌어 내었다. 근사방법으로써, Heffes의 방법과 SAM procedure를 이용하였다.

Keywords

References

  1. The Bull System Technical Journal v.52 The Interrupted Poisson Process As An Overflow Process Anatol Kuczura
  2. Operations Research v.27 Approximations for Overflows from Queues with a Finite Waiting Room John, H. Rath;Diane Sheng
  3. The Bull System Technical Journal v.59 A Class of Data Traffic Processes Covariance Function Characterization and Related Queueing Results H. Heffes
  4. IEEE Transactions on Communications v.COM-33 Individual Traffic Characteristics of Queueing Systems with Multiple Poisson and Overflow Inputs Jun Matsumoto;Yu Watanabe
  5. IEEE Transactions on Communications v.37 The Analysis of a Quene Arising in Overflow Models Kethleen S. Meier-Hellstern
  6. IEEE Transactions on Communications v.38 Overflow Analysis for Finite Waiting Room Systems Roch Guerin;Luke Y. C. Lien
  7. IEEE Journal on Seleted Areas in Communications v.9 Loss Performance Analysis of an ATM Multiplexer Loaded with High-Speed ON-OFF Sources Andrea Baiocchi;Nicola Blefari Melazzi;Marco Listanti;Aldo Roveri;Roberto Winkler