Abstract
The analysis of open queueing networks by decomposition has developed to include more detailed and generalized representation forms of traffic. We investigate this method concerning its preconditions and requirements for ATM network modelling. We use discrete time semi-Markovian processes (SMP) to characterize traffic with short-term as well as long-term autocorrelation, and to evaluate the performance of ATM switches with non-renewal input. Basic results are summarized for the autocorrelation function of semi-Markov processes, which show how to represent autocorrelated traffic by an adequate SMP model of limited size.
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References
G.R. Bitran and S. Dasu, A review of open queueing network models of manufacturing systems, Queueing Systems 12 (1992) 95–134.
G.R. Bitran and S. Dasu, Approximating nonrenewal processes by Markov chains: Use of super-Erlang (SE) chains, Opsn. Res. 41 (1993) 903–923.
W. Ding, A unified correlated input process model for telecommunication networks, Proc. 13. Internat. Teletraffic Congress, Copenhagen, eds. A. Jensen and V.B. Iversen (1991) 539–544.
K.M. Elsayed, On the superposition of discrete-time Markov renewal processes and application to statistical multiplexing of bursty traffic sources, Proc. IEEE GLOBECOM (1994) 1113–1117.
W.K. Grassmann and J.L. Jain, Numerical solutions of the waiting time distribution and idle time distribution of the arithmetic GI/G/1 queue, Operations Research 37 (1989) 141–150.
G. Haßlinger, A polynomial factorization approach to the discrete time GI/G/1/(N) queue size distribution, Performance Evaluation 23 (1995) 217–240.
G. Haßlinger, Semi-Markovian modelling and performance analysis of variable rate traffic in ATM networks, to appear in Telecommunication Systems, selected paper issue of the 3. INFORMS Telecom. Conf.
G. Haßilinger and M. Adam, Modelling and performance analysis of traffic in ATM networks including autocorrelation, Proc. IEEE Infocom'96 Conference, San Francisco (1996) 1460–1467.
G. Haßlinger and E.S. Rieger, Analysis of open discrete time queueing networks: A refined decomposition approach, J. Opl. Res. Soc. 47 (1996) 640–653.
B.R. Haverkort, Approximate analysis of networks of Ph/Ph/1/K queues: Theory & tool support, Proc. Performance Tools/MMB '95, Lecture Notes in Comp. Sci. 977, Springer (1995) 239–253.
J.J. Hunter, Mathematical techniques of applied probability, Vol. 1/2, Academic Press, New York (1983).
M.A. Johnson, An empirical study of queueing approximations based on phase-type distributions, Commun. Statist.-Stochastic Models 9, (1993) 531–561.
P.J. Kühn, Approximate analysis of general queueing networks by decomposition, IEEE Trans. on Com. COM-27 (1979) 113–126.
W.E. Leland, M.S. Taqqu, W. Millinger and D.V. Wilson, On the self-similar nature of ethernet traffic, IEEE/ACM Trasnsactions on Networking 2 (1994) 1–15.
B. Maglaris, D. Anastassiou, P. Sen, G. Karlsson and J. Robbins, Performance Models of Statistical Multiplexing in Packet Video Communications, IEEE Trans. on Com. COM-36 (1988) 834–843.
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models, J. Hopkins (1981)
M. Parulekar and A. Makowski, Tail probabilities for a multiplexer with self-similar traffic, Proc. IEEE Infocom'96 Conference, San Francisco (1996) 1452–1459.
V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modelling, IEEE/ACM Trasnsactions on Networking 3 (1995) 226–244.
B. Pourbabai, Tandem behaviour of a telecommunication system with repeated calls: A Markovian case with buffers, J. Opl. Res. Soc. 40 (1989) 671–680.
S.V. Raghavan, D. Vasukiammaiyar and G. Haring, Hierarchical approach to building generative networkload models, Computer Networks and ISDN Systems 27 (1991) 1193–1206.
E.S. Rieger and G. Haßlinger, An analytical solution to the discrete time single server queue with semi-Markovian arrivals, Queueing Systems 18 (1994) 69–105.
F. Schwarzkopf, Cell scattering among bursty ATM traffic on virtual circuits and paths (in german) diploma thesis, TH Darmstadt (1995).
B. Sengupta, The semi-Markovian queue: Theory and applications, Commun. Statist.-Stochastic Models 6 (1990) 383–413.
K. Sriram and W. Whitt, Characterizing superposition arrival processes in packet multiplexers for voice and data, IEEE J. Sel. Areas in Com. SAC-4 (1986) 833–846.
H.C. Tijms, Heuristics for the loss probability in finite-buffer queues, Proc. Conf. on Appl. Prob. in Engineering, Computer and Comm. Sciences, Paris (1993) 156–157.
W. Whitt, The queueing network analyser, Bell Syst. Techn. J. 62 (1983) 2779–2843.
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© 1997 Springer-Verlag Berlin Heidelberg
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Haßlinger, G. (1997). Towards an analytical tool for performance modelling of ATM networks by decomposition. In: Marie, R., Plateau, B., Calzarossa, M., Rubino, G. (eds) Computer Performance Evaluation Modelling Techniques and Tools. TOOLS 1997. Lecture Notes in Computer Science, vol 1245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022199
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DOI: https://doi.org/10.1007/BFb0022199
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