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Relationships and decomposition in the delayed bernoulli feedback queueing system

Published online by Cambridge University Press:  14 July 2016

D. König  and
M. Miyazawa
D. König*
Affiliation:
Bergakademie Freiberg
M. Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Sektion Mathematik, Bergakademie Freiberg, DDR-9200 Freiberg (Sachs), GDR.
∗∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda City, Chiba 278, Japan.
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Abstract

For the delayed Bernoulli feedback queue with first come–first served discipline under weak assumptions a relationship for the generating functions of the joint queue-length distribution at various points in time is given. A decomposition for the generating function of the stationary total queue length distribution has been proven. The Laplace-Stieltjes transform of the stationary joint workload distribution function is represented by its marginal distributions. The arrival process is Poisson, renewal or arbitrary stationary, respectively. The service times can form an i.i.d. sequence at each queue. Different kinds of product form of the generating function of the joint queue-length distribution are discussed.

Keywords

DELAYED BERNOULLI FEEDBACK QUEUESTEADY STATE DISTRIBUTIONBASIC EQUATIONQUEUE LENGTHWORK LOADDECOMPOSITIONAPPROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 169 - 183
Copyright
Copyright © Applied Probability Trust 1988 

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References

Disney, R. L. and König, D. (1985) Queueing networks: A survey of their random processes. SIAM Rev. 27, 335–403.CrossRefGoogle Scholar
Foley, R. D. and Disney, R. L. (1983) Queues with delayed feedback. Adv. Appl. Prob. 15, 162–182.Google Scholar
Franken, P., König, D., Arndt, U. and Schmidt, V. (1982) Queues and Point Processes. Wiley, Chichester.Google Scholar
Jackson, J. R. (1957) Networks of waiting lines. Operat. Res. 5, 518–521.Google Scholar
Kleinrock, L. (1974) Queueing Systems, Volume 1: Theory. Wiley, New York.Google Scholar
König, D. (1980) Methods for proving relationships between stationary characteristics of queueing systems with point processes. EIK 16, 10–12; 512–543.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
König, D. and Schmidt, V. (1984) Relationships between various stationary characteristics in feedback queues generated by a general class of marked point processes. Izvest. Akad. Nauk SSSR, Techn. Kibernet. No. 2, 110–114 (in Russian).Google Scholar
König, D. and Schmidt, V. (1985a) Stationary queue-length characteristics in queues with delayed feedback. J. Appl. Prob. 22, 394–407.Google Scholar
König, D. and Schmidt, V. (1985b) Limit theorems for single server feedback queueing systems with random marked point processes. Theory Prob. Appl. 30, 671–678.Google Scholar
Miyazawa, M. (1983) The derivation of invariance relations in complex queueing systems with stationary inputs. Adv. Appl. Prob. 15, 874–885.Google Scholar
Miyazawa, M. (1985) The intensity conservation law for queues with randomly changed service rate. J. Appl. Prob. 22, 408–418.Google Scholar
Miyazawa, M. (1986) Approximation of the queue-length distribution of an M/GI/s queue by the basic equations. J. Appl. Prob. 23, 443–458.Google Scholar