Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T13:14:28.106Z Has data issue: false hasContentIssue false
  • English
  • Français

On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions

Published online by Cambridge University Press:  14 July 2016

Dieter König ,
Masakiyo Miyazawa  and
Volker Schmidt
Dieter König*
Affiliation:
Bergakademie Freiberg
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
Volker Schmidt*
Affiliation:
Bergakademie Freiberg
*
∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, 92 Freiberg (Sachs), DDR.
∗∗ Postal address: Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo, Noda City, Chiba 278, Japan.
∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, 92 Freiberg (Sachs), DDR.
Get access Rights & Permissions [Opens in a new window]

Abstract

For several queueing systems, sufficient conditions are given ensuring that from the coincidence of some time-stationary and customer-stationary characteristics of the number of customers in the system such as idle or loss probabilities it follows that the arrival process is Poisson.

Keywords

STATIONARY CHARACTERISTICSQUEUE LENGTHINPUT IDENTIFICATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 860 - 871
Copyright
Copyright © Applied Probability Trust 1983 

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

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability Models. Holt, Rinehart and Winston, New York.Google Scholar
Disney, R. L., König, D. and Schmidt, V. (1984) Stationary queue length and waiting time distributions in single-server feedback queues. Adv. Appl. Prob. 16 (2).Google Scholar
Franken, P., König, D., Arndt, U. and Schmidt, V. (1981) Queues and Point Processes. Akademie-Verlag, Berlin.Google Scholar
Karr, A. F. (1981) Extreme points of certain sets of probability measures, with applications. Techn. Rep. No. 348 (June 1981), Dept. Math. Sci., The Johns Hopkins University, Baltimore.Google Scholar
König, D. and Schmidt, V. (1980) Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes. J. Appl. Prob. 17, 753–767.Google Scholar
Kuczura, A. (1973) Piecewise Markov processes. SIAM J. Appl. Math. 24, 169–181.Google Scholar
Melamed, B. (1982) On Markov jump processes imbedded at jump epochs and their queueing-theoretic applications. Math. Operat. Res. 7, 111–128.CrossRefGoogle Scholar
Miyazawa, M. (1982) Simple derivation of invariance relations and their applications. J. Appl. Prob. 19, 183–194.Google Scholar
Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models. The Johns Hopkins University Press, Baltimore.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories. Wiley, New York.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar