
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Annie Cuyt, R.B. Lenin, Gert Willems, Chris Blondia, Peter Rousseeuw, "Computing Packet Loss Probabilities in Multiplexer Models Using Rational Approximation," IEEE Transactions on Computers, vol. 52, no. 5, pp. 633644, May, 2003.  
BibTex  x  
@article{ 10.1109/TC.2003.1197129, author = {Annie Cuyt and R.B. Lenin and Gert Willems and Chris Blondia and Peter Rousseeuw}, title = {Computing Packet Loss Probabilities in Multiplexer Models Using Rational Approximation}, journal ={IEEE Transactions on Computers}, volume = {52}, number = {5}, issn = {00189340}, year = {2003}, pages = {633644}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1197129}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Computing Packet Loss Probabilities in Multiplexer Models Using Rational Approximation IS  5 SN  00189340 SP633 EP644 EPD  633644 A1  Annie Cuyt, A1  R.B. Lenin, A1  Gert Willems, A1  Chris Blondia, A1  Peter Rousseeuw, PY  2003 KW  Statistical multiplexing KW  Markovian arrival process KW  matrixanalytic methods KW  NewtonPadé approximation. VL  52 JA  IEEE Transactions on Computers ER   
Abstract—A statistical multiplexer is a basic model used in the design and the dimensioning of communication networks. The multiplexer model consists of a single server queue with constant service time and a more or less complicated arrival process. The aim is to determine the packet loss probability as a function of the capacity of the buffer. In this paper, we show how rational approximation techniques may be applied to compute the packet loss efficiently. The approach is based on the knowledge of a limited number of sample values, together with the decay rate of the probability distribution function. A strategy is proposed where the sample points are chosen automatically. The accuracy of the approach is validated by comparison with both analytical results obtained using a matrixanalytic method and simulation results.
[1] A. Baiocchi, “Analysis of the Loss Probability of the MAP/G/1/K Queue, Part I: Asymptotic Theory,” Comm. Statistical Stochastic Models, vol. 10, no. 4, pp. 867893, 1994.
[2] C. Blondia, “A DiscreteTime Batch Markovian Arrival Process as BISDN Traffic Model,” Belgian J. Operations Research, Statistics and Computer Science, vol. 32, nos. 3,4, 1992.
[3] C. Blondia and O. Casals, “Performance Analysis of Statistical Multiplexing of VBR Sources: A MatrixAnalytical Approach,” Performance Evaluation, vol. 16, pp. 520, 1992.
[4] C.S. Chang, P. Heidelberger, S. Juneja, and P. Shahabuddin, “Effective Bandwidth and Fast Simulation of ATM Intree Networks,” Proc. Performance '93, Oct. 1993.
[5] A.I. Elwalid and D. Mitra, “Analysis, Approximations and Admission Control of a MultiService Multiplexing System with Priorities,” Proc. INFOCOM '95, pp. 463472, 1995.
[6] E. Falkenberg, “On the Asymptotic Behavior of the Stationary Distribution of Markov Chains of M/G/1Type,” Comm. Statistical Stochastic Models, vol. 10, pp. 7597, 1994.
[7] J. Garcia and O. Casals, “A Discrete Time Queueing Model to Study the Cell Delay Variation in an ATM Network,” Performance Evaluation, vol. 21, pp. 322, 1994.
[8] W.B. Gong and H. Yang, “On Global Rational Approximants for Stochastic Discrete Event Systems,” Int'l J. Discrete Event Dynamic Systems, vol. 7, no. 1, 1997.
[9] A.E. Kamal, “Efficient Solution of Multiple Server Queues with Application to the Modeling of ATM Concentrators,” Proc. IEEE Infocom '96, pp. 248254, Mar. 1996
[10] G. Kemeny and J. Snell, Finite Markov Chains. New York: van NostrandReinhold, 1960.
[11] Z. Liu, P. Nain, and D. Towsley, “Exponentially Bounds with an Application to Call Admission,” Technical Report TR9463, Computer Science Dept., Univ. of Massachusetts, Amherst, Oct. 1994.
[12] M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and their Applications. Marcel Dekker, 1989.
[13] T. Thiele, Interpolationsrechnung. Leipzig: Teubner, 1909.
[14] D. Warner, “Hermite Interpolation with Rational Functions,” PhD thesis, Univ. of California, 1974.
[15] H. Wallin, “Potential Theory and Approximation of Analytic Functions by Rational Interpolation,” Proc. Colloquium Compl. Anal. at Joensuu, Lecture Notes in Math., vol. 747, pp. 434450, 1979.
[16] J.L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain. Providence, R.I.: Am. Math. Soc. Press, 1969.
[17] S. Witterrongel and H. Bruneel, “DiscreteTime Queues with Correlated Arrivals and Constant Service Times,” Computers and Operations Research, vol. 26, pp. 93108, 1999.
[18] K. Wuyts and R.K. Boel, “A Matrix Geometric Algorithm for Finite Buffer Systems with BISDN Applications,” Proc. ITC Specialists Seminar Control in Comm., pp. 265276, 1996.
[19] K. Wuyts and R.K. Boel, “Efficient Matrix Geometric Techniques for Performance Evaluation of ATM Buffers, Using Kronecker Product Structures and Spectral Decomposition,” submitted, 1997.
[20] Y. Xiong and H. Bruneel, “A Unifying Queueing Model for ATM and Its Analysis,” Int'l J. Comm. Systems, vol. 9, pp. 253267, 1996.
[21] H. Yang, “Global Rational Approximation for Computer Systems and Communication Networks,” PhD thesis, Computer Science Dept., Univ. of Massachusetts, Amherst, 1996.