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Analysis of finite-capacity polling systems

Published online by Cambridge University Press:  01 July 2016

Hideaki Takagi
Hideaki Takagi*
Affiliation:
IBM Tokyo Research Laboratory
*
∗Postal address: Tokyo Research Laboratory, IBM Japan, Ltd., No. 36 Kowa Building, 5–19 Sanban-cho, Chiyoda-ku, 102, Japan.
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Abstract

We consider a system of N finite-capacity queues attended by a single server in cyclic order. For each visit by the server to a queue, the service is given continuously until that queue becomes empty (exhaustive service), given continuously only to those customers present at the visiting instant (gated service), or given to only a single customer (limited service). The server then switches to the next queue with a random switchover time, and administers the same type of service there similarly. For such a system where each queue has a Poisson arrival process, general service time distribution, and finite capacity, we find the distribution of the waiting time at each queue by utilizing the known results for a single M/G/1/K queue with multiple vacations.

Keywords

QUEUESFINITE-CAPACITY QUEUESCYCLIC SERVICEVACATION MODELSPOLLING MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 2 , June 1991 , pp. 373 - 387
Copyright
Copyright © Applied Probability Trust 1991 

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References

Courtois, P. J. (1980) The M/G/1 finite capacity queue with delays. IEEE Trans. Comm. 28, 165–172.Google Scholar
Doshi, B. T. (1986) Queueing systems with vacations—a survey. Queueing Systems 1, 29–66.CrossRefGoogle Scholar
Doshi, B. T. (1990) Single-server queues with vacations. In Stochastic Analysis of Computer and Communication Systems , ed. Takagi, H., pp. 217–265. Elsevier, Amsterdam.Google Scholar
Ganz, A. and Chlamtac, I. (1988) Queueing analysis of finite buffer token networks. Performance Eval. Rev. 16, 30–36.Google Scholar
Ibe, O. C. and Cheng, X. (1986) Analysis of polling systems with single-message buffers. Proc. IEEE Global Telecommunications Conf. (GLOBECOM '86) , 939–943.Google Scholar
Ibe, O. C. and Trivedi, K. S. (1990) Stochastic Petri net models of polling systems. IEEE J. Sel. Areas Comm. CrossRefGoogle Scholar
Lee, T. T. (1984) M/G/1/N queue with vacation time and exhaustive service discipline. Operat. Res. 32, 774–784.Google Scholar
Lee, T. T. (1989) M/G/1/N queue with vacation time and limited service discipline. Performance Eval. 9, 181–190.Google Scholar
Robillard, P. N. (1974) An analysis of a loop switching system with multirank buffers based on the Markov process. IEEE Trans. Comm. 22, 1772–1778.CrossRefGoogle Scholar
Takagi, H. (1988) Queueing analysis of polling models. ACM Computing Surveys 20, 5–28.Google Scholar
Takagi, H. (1990) Queueing analysis of polling models: An update: In Stochastic Analysis of Computer and Communication Systems , ed. Takagi, H., pp. 267–318. Elsevier, Amsterdam.Google Scholar
Takine, T., Takahashi, Y., and Hasegawa, T. (1988) Exact analysis of asymmetric polling system with single buffers. IEEE Trans. Comm. 36, 1119–1127.CrossRefGoogle Scholar
Takine, T., Takahashi, Y., and Hasegawa, T. (1989) M/G/1/N queues with vacation and gated k-limited service. Technical report, Department of Applied Mathematics and Physics, Kyoto University.Google Scholar
Tran-Gia, P. and Raith, T. (1988) Performance analysis of finite capacity polling systems with nonexhaustive service. Performance Eval. 9, 1–16.Google Scholar