Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-23T06:37:58.450Z Has data issue: false hasContentIssue false
  • English
  • Français

A convexity result for single-server exponential loss systems with non-stationary arrivals

Published online by Cambridge University Press:  14 July 2016

Antony Svoronos  and
Linda Green
Antony Svoronos*
Affiliation:
Columbia University
Linda Green
Affiliation:
Columbia University
*
∗ Postal address: Graduate School of Business, Uris Hall, Columbia University, New York, NY 10027, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider single-server loss systems with exponential service times and non-stationary Poisson input. We prove that if the arrival rate is given by a periodic function, the proportion of lost customers is convex increasing in the amplitude.

Keywords

PERIODIC ARRIVAL RATEAMPLITUDE OF ARRIVAL RATEROSS'S CONJECTURE
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 224 - 227
Copyright
Copyright © Applied Probability Trust 1988 

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

Heyman, D. P. (1982) On Ross's conjectures about queues with non-stationary Poisson arrivals. J. Appl. Prob. 19, 245–249.CrossRefGoogle Scholar
Heyman, D. P. and Whitt, W. (1984) The asymptotic behavior of queues with time-varying arrival rates. J. Appl. Prob. 21, 143–156.CrossRefGoogle Scholar
Rolski, T. (1981) Queues with non-stationary input stream: Ross's conjecture. Adv. Appl. Prob. 13, 603–618.CrossRefGoogle Scholar
Rolski, T. (1983) Comparison theorems for queues with dependent interarrival times. Proceedings of the International Seminar , Paris, France.Google Scholar
Ross, S. M. (1978) Average delay in queues with non-stationary Poisson arrivals. J. Appl. Prob. 15, 602–609.CrossRefGoogle Scholar