Abstract
Many problems in management science and telecommunications can be solved by the analysis of aD X/Dm/1 queueing model. In this paper, we use the zeros, both inside and outside the unit circle, of the denominator of the generating function of the model to obtain an explicit closed-form solution for the equilibrium probabilities of the number of customers in the system. The moments of the number of customers in the queue or in the system are also studied. When there are infinitely many zeros outside the unit circle, we propose an approximation method using polynomials. This method yields correct values for a finite number of the probabilities, the number depending on the degree of the polynomial approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P.E. Boudreau, J.S. Griffin, Jr. and Mark Kac, An elementary queueing problem, Am. Math. Monthly 69 (1962) 713–724.
C. Bisdikian, J.S. Lew and A.N. Tantawi, The generalized D[X]/D/1 queue and its application in the analysis of bridged high speed token-ring networks, IBM Research Report, RC 18387, IBM Research Division, T.J. Watson Research Center (1992).
E.M. Spiegel, C. Bisdikian and A.N. Tantawi, Characterization of the traffic on high-speed token-ring networks, Perform. Eval. (1994) 47–72.
Y. Zhao and L.L. Campbell, Performance analysis of a multibeam packet satellite system using random access techniques, to appear in Perform. Eval.
Y. Zhao and L.L. Campbell, The explicit solution of theDX/Dm/1 model,Advances in Management Science, ed. Zhaomai Lou (Int. Academic Publ, 1994) pp. 392–396.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhao, Y.Q., Campbell, L.L. Equilibrium probability calculations for a discrete-time bulk queue model. Queueing Syst 22, 189–198 (1996). https://doi.org/10.1007/BF01159401
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01159401