Large Deviations Approximations for Fluid Queues Fed by a Large Number of On/Off Sources

A general logarithmic equivalent is given for the stationary complementary distribution function of a fluid queue fed by a large number of on/off sources. Close asymptotic approximations are also provided. These approximations are numerically validated and applied to the dimensioning of an ATM multiplexer offered variable bit rate sources of general on/off type. >

[1]  Jorma T. Virtamo,et al.  The Superposition of Variable Bit Rate Sources in an ATM Multiplexer , 1991, IEEE J. Sel. Areas Commun..

[2]  H. Daniels.  Saddlepoint Approximations in Statistics , 1954 .

[3]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[4]  J. Morrison.  Asymptotic analysis of a data-handling system with many sources , 1989 .

[5]  Debasis Mitra,et al.  Effective bandwidth of general Markovian traffic sources and admission control of high speed networks , 1993, TNET.

[6]  Jacky Guibert,et al.  Overflow probability upper bound for heterogeneous fluid queues handling general on-off sources , 1994 .

[7]  Brahim Bensaou,et al.  Performance of an ATM multiplexer queue in the fluid approximation using the Beneš approach , 1994, Ann. Oper. Res..

[8]  Thomas E. Stern,et al.  Analysis of separable Markov-modulated rate models for information-handling systems , 1991, Advances in Applied Probability.

[9]  Edward G. Coffman,et al.  Controlled stochastic model of a communication system with multiple sources , 1991, IEEE Trans. Inf. Theory.

[10]  Alain Simonian,et al.  Large Deviations Approximation for Fluid Queues Fed by a Large Number of on/off Sources , 1994 .

[11]  Hamid Ahmadi,et al.  Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks , 1991, IEEE J. Sel. Areas Commun..

[12]  James A. Bucklew,et al.  Large Deviation Techniques in Decision, Simulation, and Estimation , 1990 .

[13]  A. Weiss.  A new technique for analyzing large traffic systems , 1986, Advances in Applied Probability.

[14]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[15]  Jacky Guibert,et al.  Overflow probability upper bound in fluid queues with general on-off sources , 1994 .

[16]  J. Virtamo,et al.  Transient and stationary distributions for fluid queues and input processes with a density , 1991 .

[17]  Brahim Bensaou,et al.  A Traffic Control Framework for High Speed Data Transmission , 1993, Modelling and Evaluation of ATM Networks.