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Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions

Authors: Vitalice K. Oduol

Abstract:

The paper considers a single-server queue with fixedsize batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values.

Keywords: batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060237

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References:


[1] G. N. Higginbottom, Performance Evaluation of Communication Networks, Artech House 1998
[2] H. P. Schwefel, L. Lipsky, M. Jobmann, "On the Necessity of Transient Performance Analysis in Telecommunication Networks," 17th International Teletraffic Congress (ITC17), Salvador da Bahia, Brazil, September 24-28 2001
[3] B. van Holt, C. Blondia, "Approximated Transient Queue Length and Waiting Time Distribution via Steady State Analysis", Stochastic Models 21, pp.725-744, 2005
[4] T. Hofkens, K. Spacy, C. Blondia, "Transient Analysis of the DBMAP/ G/1 Queue with an Applications to the Dimensioning of Video Playout Buffer for VBR Traffic", Proceedings of Networking, Athens Greece, 2004
[5] D. M. Lucantoni, G. L. Choudhury, W. Witt, "The Transient BMAP/PH/1 Queue", Stochastic Models 10, pp.461-478, 1994
[6] W. Böhm. S. G. Mohanty, "Transient Analysis of Queues with Heterogeneous Arrivals" , Queuing Systems, Vol.18, pp.27-45, 1994
[7] G. L. Choudhury, D. M. Lucantoni, W. Witt, "Multidimensional Transform Inversion with Application to the Transient M/G/1 Queue", Annals of Applied Probability, 4, 1994, pp.719-740.
[8] J. Abate, G. L. Choudhury, W. Whitt, "An Introduction to Numerical Transform Inversion and its Application to Probability Models" In: W. Grassman, (ed.) Computational Probability, pp. 257-323. Kluwer, Boston , 1999.
[9] L. Kelinrock, R. Gail, Queuing Systems: Problems and Solutions, John Wiley & Sons, 1996.
[10] R. G. Hohlfeld, J. I. F. King, T. W. Drueding, G. v. H. Sandri, "Solution of convolution integral equations by the method of differential inversion", SIAM Journal on Applied Mathematics, Vol. 53 , No.1 (February 1993), Pages: 154 - 167
[11] A. S. Vasudeva Murthy, "A note on the differential inversion method of Hohlfeld et al.",SIAM Journal on Applied Mathematics, Vol. 55 , No.3 (June 1995), pp. 719 - 722
[12] P. L. Bharatiya , "The Inversion of a Convolution Transform Whose Kernel is a Bessel Function", The American Mathematical Monthly, Vol. 72, No. 4. (Apr., 1965), pp. 393-397