Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-27T11:07:11.482Z Has data issue: false hasContentIssue false
  • English
  • Français

LOSS PROBABILITIES FOR THE MX/GY/1/K+B BULK QUEUE

Published online by Cambridge University Press:  19 August 2010

Remco Germs  and
Nicky Van Foreest
Remco Germs
Affiliation:
Faculty of Economics and Business, University of Groningen, 9700 AV Groningen, The Netherlands E-mail: r.germs@rug.nl
Nicky Van Foreest
Affiliation:
Faculty of Economics and Business, University of Groningen, 9700 AV Groningen, The Netherlands E-mail: r.germs@rug.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we analyze the MX/GY/1/K+B bulk queue. For this model, we consider three rejection policies: partial acceptance, complete rejection, and complete acceptance. For each of these policies, we are interested in the loss probability for an arriving group of customers and for individual customers within a group. To obtain these loss probabilities, we derive a numerically stable method to compute the limiting probabilities of the queue length process under all three rejection policies. At the end of the article we demonstrate our method by means of a numerical example.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 4 , October 2010 , pp. 457 - 471
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Asmussen, S. (2003). Applied probability and queues. Berlin: Springer-Verlag.Google Scholar
2.Chang, S., Choi, D. & Kim, T.-S. (2004). Performance analysis of a finite-buffer bulk-arrival bulk-service queue with variable server capacity. Stochastic Analysis and Applications 22(5), 1151–1173.CrossRefGoogle Scholar
3.Çinlar, E. (1975). Introduction to stochastic processes. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
4.Dudin, A., Shaban, A. & Klimenok, V. (2005). Analysis of a queue in the BMAP/G/1/N system. International Journal of Simulation: Systems, Science and Technology 6(1–2), 13–23.Google Scholar
5.Gouweleeuw, F. (1994). The loss probability in finite-buffer queues with batch arrivals and complete rejection. Probability in the Engineering and Informational Sciences 8, 221–227.CrossRefGoogle Scholar
6.Medhi, J. (2003). Stochastic models in queuing theory. San Diego: Academic Press.Google Scholar
7.Nobel, R. (1989). Practical approximations for finite-buffer queuing models with batch arrivals. European Journal of Operational Research 38, 44–55.CrossRefGoogle Scholar
8.Perry, D. & Asmussen, S. (1995). Rejection rules in the M/G/1 queue. Queueing Systems 19, 105–130.CrossRefGoogle Scholar
9.Sericola, B. & Tuffin, B. (1999). A fluid queue driven by a Markovian queue. Queueing Systems 31, 253–264.CrossRefGoogle Scholar
10.Sikdar, K. and Gupta, U. (2008). On the batch arrival batch service queue with finite buffer under server's vacation: M X/G Y/1/N queue. Computers and Mathematics with Applications 56, 2861–2873.CrossRefGoogle Scholar
11.Takagi, H. (1993). Queuing analysis: Finite systems. Amsterdam: North–Holland.Google Scholar
12.Tijms, H. (2003). A first course in stochastic models. Chichester, UK: Wiley.CrossRefGoogle Scholar