Abstract
A cyclic service system with multiple, nonidentical finite queues and gated limited service is considered. The model is an imbedded Markov chain whose state space is reduced by applying the usual independence assumption. The analysis is done by the power method. Expectations or even probability distributions of cycle lengths, transmission lengths, buffer utilization, waiting times, throughput, and blocking probabilities are computed. The results are compared with those obtained from a simulation model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
B. Bark, Numerische Analyse eines zyklischen Wartesystems, Diploma Thesis, University of Bonn, 1988.
O.J. Boxma, Two symmetric queues with alternating service and switching times, Proc. Performance ’84, Paris, 409–431.
O. J. Boxma and B. Meister, Waiting-time approximations for cyclic-service systems with switchover times, ACM Perf. Evai. Rev. 14,1 (1986) 254–262.
W. Bux, Local-area subnetworks: A performance comparison, IEEE Trans. Comm. COM-29 (1981) 1465–1473.
R. B. Cooper and G. Murray, Queues served in cyclic order, Bell Syst. Tech. J. 48 (1969) 675–689.
R. B. Cooper, Queues served in cyclic order: Waiting times, Bell Syst. Techn. J. 49 (1970) 399–413.
M. Eisenberg, Two queues with changeover times, Oper. Res. 19 (1971) 386–401.
M. Eisenberg, Queues with periodic service and changeover times, Oper. Res. 20 (1972) 440–451.
S. W. Fuhrmann and Y. T. Wang, Mean waiting time approximations of cyclic service systems with limited service, Performance ’87, P.-J. Courtois and G. Latouche (eds.) (North-Holland, Amsterdam, 1988) 253–265.
O. Hashida, Analysis of multiqueue, Rev. El. Commun. Lab. 20 (1972) 189–199.
O. Hashida and K. Ohara, Line accommodation capacity of a communication control unit, Rev. El. Commun. Lab 20 (1972) 231–239.
O. C. Ibe and X. Cheng, Analysis of polling systems with single-message buffers, Proc. of IEEE GLOBECOM ’86, Houston, TX (1986) 939–943.
A. R. Kaye, Analysis of a distributed control loop for data transmission, Proc. of 22nd Int. Symp. on Comp. Comm. Networks and Teletraffic, Polytechnic Institute of Brooklyn, NY.(1972) 47–58.
P. J. Kuehn, Multiqueue systems with nonexhaustive cyclic service, Bell. Syst. Tech. J. 58 (1979) 671–699.
M. A. Leibowitz, An approximate method for treating a class of multiqueue problems, IBM J. Res. Develop. 5 (1961) 204–209.
R. v. Mises and H. Pollaczek-Geiringer, Verfahren zur Gleichungsauflösung, ZAMM 9 (1929) 152–164.
H. Takagi, On the analysis of a symmetric polling system with single-message buffers, Perf. Evaluation, Vol. 5, No. 3 (1985) 149–157.
H. Takagi, Analysis of polling systems, (The MIT Press, Cambridge, MA, 1986).
H. Takagi, Analysis and applications of a multiqueue cyclic service system with feedback, IEEE Trans. Comm., Vol. COM-35, No. 2 (1987) 248–250.
H. Takagi, A survey of queueing analysis of polling models, Proc. of 3rd Intern. Conf. on Data Comm. Systems and their Performance, Rio de Janeiro, Brasil (1987) 277–296.
H. Takagi, Exact analysis of round-robin scheduling of services, IBM Journal of Research and Development, Vol. 31, No. 4 (1987) 484–488.
T. Takine, Y. Takahashi and T. Hasegawa, Exact analysis of asymmetric polling systems with single buffers, IEEE Trans. on Comm., Vol. COM-36, (1988).
T. Takine, Y. Takahashi and T. Hasegawa, Average message delay of an asymmetric single-buffer polling system with round-robin scheduling of services, Proc. of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Palma de Mallorca (1988) 233–243.
P. Tran-Gia and T. Raith, Approximation for finite capacity multiqueue systems, Proc. of the 3rd GI/NTG-Fachtagung, Dortmund (1985) 332–345.
R. M. Wu and Y.-B. Chen, Analysis of a loop transmission system with round-robin scheduling of services, IBM Journal of Research and Development, Vol. 19, No. 5 (1975) 486–493.
W. J. Stewart, A comparison of numerical techniques in Markov modelling, Comm. ACM 21,2 (1978) 144–152.
W. J. Stewart, A direct numerical method for queueing networks, Proc. of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna (1979).
J. Stoer, Einführung in die Numerische Mathematik (Springer Verlag, Berlin, 1976).
J. Ch. Strelen, Piecewise approximation of densities applying the principle of maximum entropy: Waiting times in G/G/1-systems, Proc. of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Palma de Mallorca (1988) 493–512.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Strelen, C., Bärk, B. (1989). An Approach to the Numerical Analysis of Multiple-Queue, Cyclic Service Systems. In: Stiege, G., Lie, J.S. (eds) Messung, Modellierung und Bewertung von Rechensystemen und Netzen. Informatik-Fachberichte, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75079-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-75079-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51713-9
Online ISBN: 978-3-642-75079-3
eBook Packages: Springer Book Archive