Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-30T23:27:20.437Z Has data issue: false hasContentIssue false
  • English
  • Français

On a random interval graph and the maximum throughput rate in the system GI/G/1/0

Published online by Cambridge University Press:  01 July 2016

Wim M. Nawijn
Wim M. Nawijn*
Affiliation:
University of Twente
*
∗Postal address: University of Twente, Faculty of Applied Mathematics, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper gives an explicit expression for the expectation of the maximum attainable fraction of served customers in the long run for the single-server loss system GI/G/1/0, under the assumption of perfect information regarding the sequences {Xi, i = 1, 2, ·· ·} and {Yi, i = 1, 2, ·· ·} of interarrival times and service times, respectively. A heavy traffic result for this fraction is obtained for the system GI/M/1/0. The general result is based on an analysis of the random interval graph corresponding to the random intervals {[Ti, Ti + Yi), i = 1, 2, ·· ·}, in which {Ti} denotes the sequence of arrival epochs.

Keywords

STABLE SETSINGLE-SERVER LOSS SYSTEMOPTIMISATION
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 945 - 956
Copyright
Copyright © Applied Probability Trust 1991 

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. Feller, W. (1957) An Introduction to Probability Theory and its Applications , Vol. I, 2nd edn. Wiley, New York.Google Scholar
2. Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II. Wiley, New York.Google Scholar
3. Frenk, H. and Steutel, F. W. (1988) Problem 211, Statist. Neerlandica 42, 145.Google Scholar
4. Golumbic, M. C. (1980) Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York.Google Scholar
5. Nawijn, W. M. (1990) Look-ahead policies for admission to a single server loss system. Operat. Res. 5, 854–862.Google Scholar
6. Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
7. Whittaker, E. T. and Watson, G. N. (1962) Modern Analysis , 4th edn. Cambridge University Press.Google Scholar
8. Widder, D. V. (1946) The Laplace Transform. Princeton University Press.Google Scholar