Predicting quality of service for traffic with long-range fluctuations

We discuss the implications of self similar models for the problem of estimating loss probabilities in networks, and their validity. We present the tail asymptotics in a queue serviced at constant rate and whose input process has long-range dependence, for example, fractional Brownian motion (FBM) with Hurst parameter H>1/2. Some heterogeneous superpositions of such sources are also treated. We examine the experimental basis for self-similar modelling. If fluctuations in traffic levels can be accounted for by variations in time-dependent external parameters, rather than statistically through parsimonious modelling by FBM, then quality of service predictions may be achieved by applications of techniques familiar for short-range dependent traffic.

[1]  Jean C. Walrand,et al.  Effective bandwidths for multiclass Markov fluids and other ATM sources , 1993, TNET.

[2]  Joseph Y. Hui.  Resource allocation for broadband networks , 1988, IEEE J. Sel. Areas Commun..

[3]  N. Duffield,et al.  Economies of scale in queues with sources having power-law large deviation scalings , 1996, Journal of Applied Probability.

[4]  Jean C. Walrand,et al.  Decoupling bandwidths for networks: a decomposition approach to resource management , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[5]  P. Glynn,et al.  Logarithmic asymptotics for steady-state tail probabilities in a single-server queue , 1994, Journal of Applied Probability.

[6]  D. Aldous.  Probability Approximations via the Poisson Clumping Heuristic , 1988 .

[7]  J. R. Wallis,et al.  Noah, Joseph, and Operational Hydrology , 1968 .

[8]  Nick Duffield,et al.  Large deviations for arrivals, departures, and overflow in some queues of interacting traffic , 1994 .

[9]  Frank P. Kelly,et al.  Effective bandwidths at multi-class queues , 1991, Queueing Syst. Theory Appl..

[10]  Nick Duffield,et al.  Large deviations and overflow probabilities for the general single-server queue, with applications , 1995 .

[11]  Nick G. Duffield,et al.  Entropy of ATM Traffic Streams: A Tool for Estimating QoS Parameters , 1995, IEEE J. Sel. Areas Commun..

[12]  Nick G. Duffield,et al.  Large deviations, the shape of the loss curve, and economies of scale in large multiplexers , 1995, Queueing Syst. Theory Appl..

[13]  Walter Willinger,et al.  Long-range dependence in variable-bit-rate video traffic , 1995, IEEE Trans. Commun..

[14]  Ward Whitt,et al.  Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues , 1993, Telecommun. Syst..

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

[16]  WillingerWalter,et al.  On the self-similar nature of Ethernet traffic , 1993 .

[17]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  A. Dembo,et al.  Large Deviation Techniques and Applications. , 1994 .

[20]  V. Klemeš.  The Hurst Phenomenon: A puzzle? , 1974 .

[21]  Richard J. Gibbens,et al.  Effective bandwidths for the multi-type UAS channel , 1991, Queueing Syst. Theory Appl..

[22]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .