Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-19T03:22:16.281Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Results for Buffer Systems under Heavy Load

Published online by Cambridge University Press:  27 July 2009

J. C. W. Van Ommeren  and
A. G. de Kok
J. C. W. Van Ommeren
Affiliation:
Department of EconometricsFree University, The Netherlands
A. G. de Kok
Affiliation:
Centre for Quantitative MethodsNederlandse Philips Bedrijven B. V.The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a dam (or storage) model of the GI/G/I type with a finite capacity K. An arriving input being larger than the unfilled capacity of the dam causes an overflow where the excess amount is lost. Important performance measures for this system are the overflow probability and the long-run fraction of input that is lost. We give asymptotic expansions for these measures for large K both for the case of a load factor less than 1 and for the case of a load factor larger than 1. Also, related results are obtained for the impatient customer model of the M/G/l type.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 3 , July 1987 , pp. 327 - 348
Copyright
Copyright © Cambridge University Press 1987

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

1Cohen, J. W. (1976). on regenerative processes in queueing theory. Berlin: Springer Verlag.Google Scholar
2Cohen, J. W. (1982). The single server queue. Amsterdam: North-Holland.Google Scholar
3de, Kok A. G. and Tijms, H. C.. (1985). A queueing system with impatient customers. J. Appl. Prob. 22: 688–696.Google Scholar
4de, Kok A. G. (1987). Production-inventory control models; Approximations and algorithms (CWI Tract. No. 30). Amsterdam: CWI.Google Scholar
5Feller, W. (1971). An introduction to probability theory and its application (vol. II). New York: Wiley.Google Scholar
6Iglehart, D. L. (1972). Extreme values in the Gl/G/1 Queue. Ann. Math. Statist. 43: 627–635.Google Scholar
7Lemoine, A.J. (1976). On random walks and stable G1/0/1 queues. Math. Op. Res. 1: 159–164.Google Scholar
8Prabhu, N. U. (1980). Stochastic storage processes. Berlin: Springer Verlag.CrossRefGoogle Scholar
9Tijms, H. C. (1986). Stochastic modelling and analysis. A computational approach. New York: Wiley.Google Scholar
10Wolff, R. W. (1982). Poisson arrivals see time averages. Oper. Res. 30: 223–231.Google Scholar