Abstract
Important efforts have been invested to characterize the performance of an ATM multiplexer system loaded with a set of superimposed ON/OFF sources, since this ON/OFF source model has been extensively used as a coarse approximation of variable bitrate services (e.g. shaped LAN traffic). Literature exists on approximations for queueing systems, in which a large number of superimposed sources is considered, and replaced by a more tractable aggregate model. In this contribution, the focus is set on a discrete-time technique related to exact results for the ON-OFF[N]/D/1 queueing system with infinite queueing capacity for the superposition of a small number of such sources. The discrete-time batch Markovian arrival process (D-BMAP) Queue Input Process (QIP) is first introduced. Complete solutions for the D-BMAP/D/1 queueing system with normalised service time are provided in terms of the system occupancy distribution, its moments, the sojourn time distribution and its moments. A proposal for expressing an aggregate of ON/OFF sources QIP as a D-BMAP is then formulated, and the sparsity of the matrices and vectors highlighted. Finally, the degenerate cases corresponding to no multiplexing gain (“underload” case), the superposition of two-state Markov sources (2SM) and Bernoulli sources are handled, and closed form expressions for the moments provided.
This research was supported by the Swiss Federal Office of Education and Science (OFES) within a funding for project RACE 2024 entitled “Broadband Access Facilities”.
Chapter PDF
References
A. Baiocchi et al., “Loss Performance Analysis of an ATM Multiplexer Loaded with High-Speed On-Off Sources”, IEEE JSAC, vol. 9, no. 3, pp. 388–393, April 1991.
C. Blondia and O. Casals, “Statistical Multiplexing of VBR Sources: a Matrix-Analytic Approach”, Performance Evaluation, vol. 16, pp. 5–20, 1992.
U. Briem, T. Theimer, and H. Kröner, “A General Discrete-Time Queueing Model: Analysis and Applications”, in International Teletraffic Congress 13 (ITC-13), pp. 1319, A. Jensen and V.B.I. editor, Elsevier Science Publishers B.V., 1991.
H. Bruneel, “Queueing Behavior of Statistical Multiplexers with Correlated Inputs”, IEEE Transactions on Communications, vol. 36, no. 12, pp. 1339–341, December 1988.
H. Kröner, “Statistical Multiplexing of Sporadic Sources-Exact and Approximate Performance Analysis”, in Proc. of 13th International Teletraffic Congress (ITC 13), pp. 787–793, A. Jensen and V.B.I. editor, Elsevier Science Publishers B.V., Copenhagen, Denmark, June 1991.
S.Q. Li, “Generating Function Approach for Discrete Queueing Analysis with Decomposable Arrival and Service Markov Chains”, in INFOCOM’92, pp. 2168–2177, Florence, Italy, May 6–8 1992.
D.M. Lucantoni, “New Results on the Single Server Queue with a Batch Markovian Arrival Process”, Communications in Statistics-Stochastic Models, vol. 7, pp. 1–46, 1991.
D.M. Lucantoni, BMAP/G/1 Queue: A Tutorial,vol. 729, Lecture Notes in Computer Science. L. Donatiello and R. Nelson Ed., pp. 330–358.
M. Luoni, “ATM Traffic Characterization with Applications to Connection Acceptance Control”, Ph.D. thesis, Thèse no 979 (1991), Ecole Polytechnique Fed. de Lausanne, DE-TCOM, 1991.
M.F. Neuts, Structured Stochastic Matrices of MIGI1 Type and their Applications. New York and Basel: Marcel Dekker, Inc., 1989, Probability: Pure and Applied-A series of Textbooks and Reference Books.
M. Neuts, “On Viterbi s Formula for the Mean Delay in a Queue of Data Packets”, Commun.Statist.-Stochastic Models, vol. 6, no. 1, pp. 87–98, 1990.
R. Slosiar, “Moments of the Queue Occupancy in an ATM Multiplexer Loaded with ON/OFF Sources”, in Proc. of the IEEE Singapore International Conference on Communication Systems (ICCS ‘84), vol. 2 /3, pp. 754–759, November 14–18 1994.
R. Slosiar, “Busy and Idle Periods at an ATM Multiplexer Output Resulting from the Superposition of Homogeneous ON/OFF Sources”, in Proc. of 14th Internantional Teletraffic Congress, vol. vol. la, pp. 431–440, J. Labetoulle and J.W.R. Editors, Elsevier pubi., Antibes, France, 6–10th June 1994.
R. Slosiar, “Performance Analysis Methods of ATM-Based Broadband Access Networks using Stochastic Traffic Models”, Ph.D. thesis, to appear, EPFL, DETCOM, CH-1015 Lausanne, 1995.
A.M. Viterbi, “Approximate Analysis of Time-Synchronous Packet Networks”, IEEE JSAC, vol. 4, no. 6, pp. 879–890, April 1986.
Y. Xiong, “Analysis of the Asymptotic Queueing Behavior of Statistical Multiplexers with General Markov-Modulated Traffic Sources”, Ph.D. thesis, Faculty of Applied Sciences, University of Gent, 1994.
Z. Mang, “Analysis of a Discrete-Time Queue with Integrated Bursty Inputs in ATM Networks”, International Journal of Digital and Analog Communication Systems, vol. 4, pp. 191–203, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Slosiar, R. (1995). Exact Results for an ATM Multiplexer with Infinite Queue Loaded with Batch Markovian Arrivals. In: Kouvatsos, D.D. (eds) Performance Modelling and Evaluation of ATM Networks. ATM 1994. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34881-0_16
Download citation
DOI: https://doi.org/10.1007/978-0-387-34881-0_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6164-1
Online ISBN: 978-0-387-34881-0
eBook Packages: Springer Book Archive