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Abstract: We consider from a thermodynamic viewpoint queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (a t ; v t ; t 2 R+ ) and a rate function I such that if (W t ; t 2 R+ ) denotes the workload process, then lim t!1 v \Gamma1 t log P (W t =a t ? w) = \GammaI (w) on the continuity set of I . In the case that a t = v t = t it has been argued heuristically, and recently proved in a... (Update)
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BibTeX entry: (Update)
N. G. Duffield and N. O. Connell. Large deviations and overflow probabilities for the general single server queue, with applications. To appear in Proc. Cam. Phil. Soc.; available as: ftp:stp01.stp.dias.ie/DAPG/dapg9330.ps. http://citeseer.ist.psu.edu/article/duffield94large.html More
@misc{ duffield-large,
author = "N. Duffield and N. Connell",
title = "Large deviations and overflow probabilities for the general single server
queue",
text = "N. G. Duffield and N. O. Connell. Large deviations and overflow probabilities
for the general single server queue, with applications. To appear in Proc.
Cam. Phil. Soc.; available as: ftp:stp01.stp.dias.ie/DAPG/dapg9330.ps.",
url = "citeseer.ist.psu.edu/article/duffield94large.html" }
Citations (may not include all citations):1120 Handbook of Mathematical Functions (context) - Abramowitz, Stegun - 1965
220 A storage model with self-similar input - Norros - 1994
214 Large Deviation Techniques and Applications (context) - Dembo, Zeitouni - 1993
142 Effective bandwidths for multiclass Markov fluids and other .. - Kesidis, Walrand et al. - 1993
124 Lectures on the Coupling Method (context) - Lindvall - 1992
111 Logarithmic asymptotics for steady-state tail probabilities .. - Glynn, Whitt - 1993
76 Probability Approximations via the Poisson Clumping Heuristi.. - Aldous - 1989
46 Asymptotic Methods in Queueing Theory (context) - Borovkov - 1984
45 The superposition of variable bitrate sources in ATM multipl.. (context) - Norros, Roberts et al. - 1991
41 Fractional Brownian motions (context) - Mandelbrot, Van Ness - 1968
25 Exponential bounds for queues with Markovian arrivals (context) - Duffield - 1993
16 Thermodynamic probability theory: some aspects of large devi.. - Lewis, Pfister - 1994
14 A decomposition of Bessel bridges (context) - Pitman, Yor - 1982
12 Fluid model driven by an Ornstein-Uhlenbeck process (context) - Kulkarni, Rolski - 1993
7 queue length and delay of deterministic and stochastic queue.. (context) - Chang - 1993
7 Ethernet traffic is self-similar: stochastic modelling of pa.. (context) - Leland, Taqqu et al. - 1993
6 Sample behaviour of Gaussian processes (context) - Marcus, Shepp - 1972
6 Studies on a model for connectionless traffic (context) - Norros - 1993
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