Abstract
This paper is concerned with establishing Poisson approximations to flows in general queueing networks. Bounds are provided to assess the departure of a given flow from Poisson and these lead to simple criteria for good Poisson approximations. The class of networks considered here are those with a countable collection of customer classes and where the service requirement of a customer at a given queue has a general distribution which may depend upon the class of the customer.
Keywords
- Queueing networks
- Poisson Approximations
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
BARBOUR, A.D. (1976), Networks of queues and a method of stages, Adv. Appl. Prob., 8, 584–591.
BROWN, T.C. (1982) Some Poisson Approximations, Statistics Research Report, Dept. of Maths. Monash University.
BROWN, T.C. and POLLETT, P.k. (1982) Some Distributional Approximations in Markovian Queueing Networks, Adv. Appl. Prob., 14, 654–671.
CHANG, A. and LAVENBERG, S.S. (1974) Work Rates in Closed Queueing Networks with General Independent Servers, Opns. Res., 22, 883–847.
COX, D.R. (1955) A use of complex probabilities in the theory of stochastic processes. Proc. Camb. Phil. Soc., 51, 313–319.
KELLY, F.P. (1976) Networks of queues, Adv. Appl. Prob., 8. 416–432.
KELLY, F.P. (1979) Reversibility and Stochastic Networks, Wiley and Sons, New York.
POLLETT, P.K. (1983) Some Poisson approximations for departure processes in general queueing networks. Submitted for publication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Pollett, P.K. (1984). Distributional approximations for networks of quasireversible queues. In: Truman, A., Williams, D. (eds) Stochastic Analysis and Applications. Lecture Notes in Mathematics, vol 1095. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099125
Download citation
DOI: https://doi.org/10.1007/BFb0099125
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13891-4
Online ISBN: 978-3-540-39103-6
eBook Packages: Springer Book Archive
