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A note on a D/G/K loss system with retrials

Published online by Cambridge University Press:  14 July 2016

Behnam Pourbabai*
Affiliation:
University of Maryland
*
Postal address: Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA.

Abstract

An algorithm is suggested for approximating the performance of a D/G/K loss system with deterministic input, generally distributed processing time, K heterogeneous servers, the random access processing discipline, and retrials in steady state. In loss systems with retrials, the units which at the instants of their arrival at the system find all the servers busy, are not lost: those units retry to be processed by merging with the incoming arrival units. In this system, a fraction of the units which have not initially been processed will be allowed to leave the system. The performance of this system in steady state is approximated by a recursive technique.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1990 

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References

Cohen, J. W. (1957) Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecomm. Rev. 18(2), 49100.Google Scholar
Falin, G. I. (1986) Single-line repeated orders queueing systems. Optimization 17, 649667.Google Scholar
Falin, G. I. (1988) On a multiclass batch arrival retrial queue. Adv. Appl. Prob. 20, 483487.Google Scholar
Gnedenko, B. V. and Kovalenko, I. N. (1968) Queueing Theory, Israel Program for Scientific Translations, Jerusalem.Google Scholar
Halfin, S. (1981) Distribution of the interoverflow time for the GI/G/1 loss system. Math. Operat. Res. 6, 563570.Google Scholar
Kuehn, P. J. (1979) Approximate analysis of general queueing networks, by decomposition. IEEE Trans. Comm. 27, 113126.Google Scholar
Nawijn, W. M. (1983) Stochastic Conveyor Systems. Ph.D. Dissertation, Twente University of Technology, Enschede.Google Scholar
Pourbabai, B. (1988a) Performance modeling of a telecommunication system with repeated calls. EIK 24, 613625.Google Scholar
Pourbabai, B. (1988b) Approximate analysis of a G/G/K queueing loss system with heterogeneous servers and retrials. Int. J. Systems Sci. 19, 10471052.Google Scholar
Pourbabai, B. and Sonderman, D. (1986) Service utilization factors in queueing systems with ordered entry and heterogeneous servers. J. Appl. Prob. 23, 236242.Google Scholar
Pritsker, A. A. B. (1966) Application of multichannel queueing results to the analysis of conveyor systems. J. Industrial Eng. 17, 1421.Google Scholar
Pritsker, A. A. B. and Pegden, C. B. (1979) Introduction to Simulation and SLAM. Halsted Press Wiley, New York.Google Scholar
Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
Whitt, W. (1982) Approximating a point process by a renewal process I: Two basic methods. Operat. Res. 30, 125147.Google Scholar