Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T00:06:37.805Z Has data issue: false hasContentIssue false
  • English
  • Français

A queueing system with impatient customers

Published online by Cambridge University Press:  14 July 2016

A. G. De Kok  and
H. C. Tijms
A. G. De Kok*
Affiliation:
Vrije Universiteit
H. C. Tijms*
Affiliation:
Vrije Universiteit
*
∗Postal address: Vrije Universiteit, Department of Actuarial Sciences and Econometrics, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
∗Postal address: Vrije Universiteit, Department of Actuarial Sciences and Econometrics, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

Keywords

APPROXIMATIONSLOSS PROBABILITYAVERAGE DELAY
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 688 - 696
Copyright
Copyright © Applied Probability Trust 1985 

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

Barrer, D. Y. (1957) Queueing with impatient customers and ordered service. Operat. Res. 5, 650–656.Google Scholar
Daley, D. J. (1965) General customer impatience in the queue GI/G/1. J. Appl. Prob. 2, 186–205.CrossRefGoogle Scholar
De Kok, A. G., Tijms, H. C. and Van Der Duyn Schouten, F. A. (1984) Approximations for the single product production-inventory problem with compound Poisson demand and service level constraints. Adv. Appl. Prob. 16, 378–401.Google Scholar
De Kok, A. G. and Tijms, H. C. (1985) A two-moments approximation for a buffer design problem requiring a small rejection probability. Performance Evaluation, 77–84.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Finch, P. D. (1960) Deterministic customer impatience in the queueing system GI/M/1. Biometrika 47, 45–52.CrossRefGoogle Scholar
Gnedenko, B. V. and Kovalenko, I. N. (1968) Introduction to Queueing Theory. Israel Program for Scientific Translations, Jerusalem.Google Scholar
Hokstad, P. (1979) A single-server queue with constant service time and restricted accessibility. Management Sci. 25, 205–208.CrossRefGoogle Scholar
Page, E. (1972) Queueing Theory in OR. Butterworths, London.Google Scholar
Schassberger, R. (1973) Warte schlangen. Springer-Verlag, Berlin.Google Scholar
Stanford, R. E. (1979) Reneging phenomena in single channel queues. Math. Operat. Res. 4, 162–178.Google Scholar
Stidham, S. Jr. (1974) A last word on L = λW . Operat. Res. 22, 417–421.Google Scholar
Tijms, H. C. (1986) Stochastic Operations Research: A Computational Approach. Wiley, New York.Google Scholar
Van Hoorn, M. H. (1981) Algorithms for the state probabilities in a general class of single server queueing systems. Management Sci. 27, 1178–1187.Google Scholar
Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.CrossRefGoogle Scholar