Advances in Applied Probability · 1986 · 130 citations · 11 references
EngineeringMathematicsProbability TheoryQueuing TheoryStochastic ProcessesLarge DeviationsQueueing TheoryTraffic EngineeringTraffic Flow TheoryTransient AnalysisTransient Flow AnalysisDynamic Transient BehaviorLarge Deviations PrincipleTraffic Flow ModelingTransient Queueing Behavior
This paper presents a new technique for analyzing the frequency of a very large class of rare events in large traffic systems. The method is based on the theory of large deviations. If n is a large parameter, typically the number of potential traffic sources, then where I is the solution to an associated variational problem. We present a new analysis of a previously solved system as well as an analysis of a previously intractable system. As by-products of our analysis, we obtain estimates of the transient behavior of the system, and show how they may be used in analyzing some flow control schemes.
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ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
A. D. Ventsel’, Mark Freidlin · Russian Mathematical Surveys · 1970 · 397 citations
Applications of Queueing Theory
Edward L. Hannan, G. F. Newell · Technometrics · 1985 · 334 citations