Abstract
In this paper, we examine a queueing problem motivated by the pipeline polling protocol in satellite communications. The model is an extension of the cyclic queueing system withM-limited service. In this service mechanism, each queue, after receiving service on cyclej, makes a reservation for its service requirement in cyclej + 1. The main contribution to queueing theory is that we propose an approximation for the queue length and sojourn-time distributions for this discipline. Most approximate studies on cyclic queues, which have been considered before, examine the means only. Our method is an iterative one, which we prove to be convergent by using stochastic dominance arguments. We examine the performance of our algorithm by comparing it to simulations and show that the results are very good.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Akashi, K. Kobayashi, J. Namiki and K. Watanabe, Pipeline polling for satellite communications, IEICE Technical Report No. CS85-66 (1984), pp. 49–54.
F. Akashi, K. Kobayashi, J. Namiki and K. Watanabe, Multipoint communication system having polling and reservation schemes, US Patent No. 4,742,512 (May 3, 1988).
O.J. Boxma and B.W. Meister, Waiting-time approximations for cyclic-service systems with switchover times, Perf. Eval. 7(1987)299–308.
W. Bux and H.L. Truong, Mean-delay approximation for cyclic service queueing systems, Perf. Eval. 3(1983)187–196.
K. Chang and D. Sandhu, Analysis of anM/G/1 queue with vacations and exhaustive limited service policy, Technical Report No. 0489, Information and Decision Systems Laboratory, Rensselaer Polytechnic Institute, Troy, NY (1989).
K. Chang and D. Sandhu, Mean waiting time approximations in cyclic-service systems with exhaustive limited service policy,INFOCOM-91 (1991), pp. 1168–1177.
R.B. Cooper and G. Murray, Queues served in cyclic order, Bell Syst. Tech. J. 48(1969)675–689.
B.T. Doshi, Queueing systems with vacation — a survey, Queueing Systems 1(1986)29–66.
M. Eisenberg, Queues with periodic service and changeover times, Oper. Res. 20(1972)440–451.
S.W. Fuhrmann, Symmetric queue served in cyclic order, Oper. Res. Lett. 4(1985)139–144.
S.W. Fuhrmann and Y.T. Wang, Analysis of cyclic service systems with limited service: Bounds and approximations, Perf. Eval. 9(1988)35–54.
L. Georgiadis and W. Szpankowski, Stability of token passing rings, Queueing Systems 11(1992), this issue.
J.F. Hayes,Modeling and Analysis of Computer Communications Networks (Plenum, New York, 1984).
D.L. Jagerman, An inversion technique for the Laplace transform, Bell. Syst. Tech. J. 61(1982) 1995–2002.
A.G. Konheim and B.W. Meister, Waiting lines and times in a system with polling, J. ACM 21(1974)470–490.
K. Kurosawa and S. Tsujii, Analysis on asymmetric polling systems with limited service,Proc. IEEE Nat. Telecommunications Conf. (1981), pp. 4.2.1–4.2.5.
M. Lang and M. Bosch, Performance analysis of finite capacity polling systems with limited-M service,Teletraffic and Datatraffic in a Period of Change, ed. A. Jensen and V.B. Iverson (North-Holland, Amsterdam, 1991).
D.S. Lee and B. Sengupta, A reservation based cyclic server with limited service.Performance'92.
T. Lee,M/G/1/N queue with vacation time and limited service discipline, Perf. Eval. 9(1988) 181–190.
K.K. Leung, Waiting time distributions for token-passing systems with limited-k service via discrete Fourier transform,Performance'90, ed. P.J.B. King, I. Mitrani and R.J. Pooley (North-Holland, Amsterdam, 1990), pp. 333–347.
K.K. Leung, Cyclic-service systems with probabilistically-limited service, IEEE J. Sel. Areas Comm. SAC-9(1991)185–193.
H. Levy, Analysis of cyclic-olling systems with binomial-gated service,Performance of Distributed and Parallel Systems, ed. T. Hasegawa, H. Takagi and Y. Takahashi (North-Holland, Amsterdam, 1989), pp. 127–139.
H. Levy, M. Sidi and O.J. Boxma, Dominance relations in polling systems, Queueing Systems 6(1990)155–172.
M. Nomura and K. Tsukamoto, Traffic analysis on polling systems, Trans. Inst. Elec. Comm. Engineers of Japan J61-B(1978)600–607.
D. Sarkar and W.I. Zangwill, Expected waiting time for non-symmetric cyclic queueing systems — exact results and applications. Manag. Sci. 35(1989)1463–1474.
L.D. Servi, Average delay approximation ofM/G/1 cyclic service queues with Bernoulli schedules, IEEE J. Sel. Areas Comm. SAC-4(1986)813–822.
M. Sidi and H. Levy, Customer routing in polling systems,Performance'90, ed. P.J.B. King, I. Mitrani and R.J. Pooley (North-Holland, Amsterdam, 1990), pp. 319–329.
D. Stoyan,Comparison Methods for Queues and Other Stochastic Models (Wiley, New York, 1983).
H. Takagi, Mean message waiting time in symmetric polling systems,Proc. Performance'84, ed. E. Gelenbe (North-Holland, Amsterdam, 1984), pp. 293–302.
H. Takagi,Analysis of Polling Systems (MIT Press, Cambridge, 1986).
H. Takagi, Queueing analysis of polling models, ACM Comput. Surveys 20(1988)5–28.
T. Takine, Y. Takahashi and T. Hasegawa, Exact analysis of asymmetric polling systems with single buffers, IEEE Trans. Comm. COM-36(1988)1119–1127.
K.S. Watson, Performance evaluation of cyclic service strategies — a survey,Proc. Performance'84, ed. E. Gelenbe (North-Holland, Amsterdam, 1984), pp. 521–533.
O. Yue and C.A. Brooks, Performance of the timed token scheme in MAP, IEEE Trans. Comm. COM-38(1990)1006–1012.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, D.S., Sengupta, B. An approximate analysis of a cyclic server queue with limited service and reservations. Queueing Syst 11, 153–178 (1992). https://doi.org/10.1007/BF01159293
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01159293