Abstract
This paper describes a new method for evaluating the queue length distribution in an ATM multiplexer assuming the cell arrival process can be assimilated to a variable rate fluid input. The method is based on a result due initially to Beneš allowing the analysis of queues with general input. Its extension to fluid input systems is considered here in the case of a superposition of on/off sources. We derive an upper bound on the complementary queue length distribution. The method is most easily applied in the case of Poisson burst arrivals (infinite sources model). In this case, we derive analytic expressions for the tail of the queue length distribution. A corrective factor is deduced to convert the upper bounds to good approximations. Numerical results justify the accuracy of the method and demonstrate the impact of certain traffic characteristics on queue performance.
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References
D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data handling system with multiple sources, Bell Syst. Tech. J. 61 (1982) 1871–1894.
V.E. Beneš,General Stochastic Processes in the Theory of Queues (Addison-Wesley, 1963).
J. Guibert, Overflow probability upper bound in the fluid queue with on/off sources, submitted (1992).
S.B. Jacobsen, K. Moth, L. Dittmann and K. Sallberg, Load control in ATM networks, in:Proc. Int. Switching Symp., Stockholm (May 1990).
L. Kleinrock,Queueing Systems, vol. 1: Theory (Wiley, 1975).
L. Kosten, Stochastic theory of a multi-entry buffer (I), Delft Progress Report series F 1 (1974) 10–18.
L. Kosten, Stochastic theory of a multi-entry buffer (II), Delft Progress Report series F 1 (1974) 44–50.
L. Kosten, Stochastic theory of data handling systems with groups of multiple sources, in:Proc. Int. Symp. on Performance of Computer Communications Systems, Zurich (March 1984).
L. Kosten, Liquid models for a type of information buffer problems, Delft Progress Report series F 11 (1986) 71–86.
H. Kröner, Statistical multiplexing of sporadic sources — exact and approximate analysis, in:Proc. 13th Int. Teletraffic Congress, Copenhagen (June 1991).
L. Kosten and O. Vreize, Stochastic theory of a multi-entry buffer (III), Delft Progress Report series F 1 (1975) 103–115.
J.D. Murray,Asymptotic Analysis (Springer, 1984).
I. Norros, J.W. Roberts, A. Simonian and J. Virtamo, The superposition of variable bitrate sources in ATM multiplexers, IEEE J. Sel. Areas Comm. SAC-9 (1991) 378–387.
A. Simonian, Stationary analysis of a fluid queue with input rate varying as an Ornstein-Uhlenbeck process, SIAM J. Appl. Math. 51 (1991).
A. Simonian and J.T. Virtamo, Transient and stationary distributions for fluid queues and input processes with a density, SIAM J. Appl. Math. 51 (1991).
K. Sriram and W. Whitt, Characterizing superposition arrival processes in packet multiplexers for voice and data, IEEE J. Sel. Areas Comm. SAC-4 (1986) 833–846.
R.C. Tucker, Accurate method for analysis of a packet speech multiplexer with limited delay, IEEE Trans. Comm. COM-36 (1988).
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Bensaou, B., Guibert, J., Roberts, J.W. et al. Performance of an ATM multiplexer queue in the fluid approximation using the Beneš approach. Ann Oper Res 49, 137–160 (1994). https://doi.org/10.1007/BF02031595
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DOI: https://doi.org/10.1007/BF02031595