Eeective Bandwidth in High Speed Digital Networks

The theory of large deviations provides a simple uniied basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theory of eeective bandwidth for high speed digital networks, especially ATM networks. This includes (i) identiication of the appropriate energy function, entropy function and eeective bandwidth function of a source, (ii) the calculus of the eeective bandwidth functions, (iii) bandwidth allocation and buuer management, (iv) traac descriptors, and (v) envelope processes and conjugate processes for fast simulations and bounds.

[1]  Michael R. Frater,et al.  Optimally efficient estimation of the statistics of rare events in queueing networks , 1991 .

[2]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[3]  Gustavo de Veciana,et al.  Bandwidth allocation for multiple qualities of service using generalized processor sharing , 1996, IEEE Trans. Inf. Theory.

[4]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

[5]  Rene L. Cruz,et al.  A calculus for network delay, Part I: Network elements in isolation , 1991, IEEE Trans. Inf. Theory.

[6]  Ward Whitt,et al.  Squeezing the Most Out of ATM , 1995, IEEE Trans. Commun..

[7]  P. Whittle A risk-sensitive maximum principle , 1990 .

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

[9]  Peter Whittle,et al.  Likelihood and cost as path integrals , 1991 .

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

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

[12]  Cheng-Shang Chang,et al.  Sample path large deviations and intree networks , 1995, Queueing Syst. Theory Appl..

[13]  Cheng-Shang Chang,et al.  Effective bandwidths of departure processes from queues with time varying capacities , 1995, Proceedings of INFOCOM'95.

[14]  Venkat Anantharam,et al.  How large delays build up in a GI/G/1 queue , 1989, Queueing Syst. Theory Appl..

[15]  Thomas L. Saaty,et al.  Elements of queueing theory , 2003 .

[16]  Rene L. Cruz,et al.  A calculus for network delay, Part II: Network analysis , 1991, IEEE Trans. Inf. Theory.

[17]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[18]  James F. Kurose,et al.  On computing per-session performance bounds in high-speed multi-hop computer networks , 1992, SIGMETRICS '92/PERFORMANCE '92.

[19]  Donald F. Towsley,et al.  Local Allocation of End-to-End Quality-of-Service in High-Speed Networks , 1993, Modelling and Evaluation of ATM Networks.

[20]  Philip Heidelberger,et al.  Fast simulation of packet loss rates in a shared buffer communications switch , 1995, TOMC.

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

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

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

[24]  Khosrow Sohraby,et al.  On the asymptotic behavior of heterogeneous statistical multiplexer with applications , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[25]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[26]  G. Parmigiani Large Deviation Techniques in Decision, Simulation and Estimation , 1992 .

[27]  HeidelbergerPhilip Fast simulation of rare events in queueing and reliability models , 1995 .

[28]  P. Whittle A risk-sensitive maximum principle: the case of imperfect state observation , 1991 .

[29]  Kwang-Cheng Chen,et al.  Group randomly addressed polling for multicell wireless data networks , 1994, Proceedings of ICC/SUPERCOMM'94 - 1994 International Conference on Communications.

[30]  Michel Mandjes,et al.  Finding the Conjugate of Markov Fluid Processes , 1995 .

[31]  D. Stroock An Introduction to the Theory of Large Deviations , 1984 .

[32]  Nsf Ncr,et al.  A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single Node Case* , 1991 .

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

[34]  R. Ellis,et al.  LARGE DEVIATIONS FOR A GENERAL-CLASS OF RANDOM VECTORS , 1984 .

[35]  J. Gärtner On Large Deviations from the Invariant Measure , 1977 .

[36]  Jay Cheng,et al.  Computable exponential bounds for intree networks with routing , 1995, Proceedings of INFOCOM'95.

[37]  George Kesidis,et al.  Quick simulation of ATM buffers , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[38]  A. Dembo,et al.  Large deviations: From empirical mean and measure to partial sums process , 1995 .

[39]  R. Ellis,et al.  Entropy, large deviations, and statistical mechanics , 1985 .

[40]  Nick G. Duffield,et al.  Exponential bounds for queues with Markovian arrivals , 1994, Queueing Syst. Theory Appl..

[41]  Jean Walrand,et al.  A quick simulation method for excessive backlogs in networks of queues , 1989 .

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

[43]  Marie Cottrell,et al.  Large deviations and rare events in the study of stochastic algorithms , 1983 .

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

[45]  Henrici Computational complex analysis , 1973 .

[46]  Philip Heidelberger,et al.  Effective Bandwidth and Fast Simulation of ATM Intree Networks , 1994, Perform. Evaluation.

[47]  J. Lynch,et al.  A weak convergence approach to the theory of large deviations , 1997 .

[48]  Alan Weiss,et al.  Large Deviations For Performance Analysis: Queues, Communication and Computing , 1995 .