Stochastic NetworksThis IMA Volume in Mathematics and its Applications STOCHASTIC NETWORKS is based on the proceedings of a workshop that was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We thank Frank P. Kelly and Ruth J. Williams for organizing the workshop and for editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Air Force Office of Scientific Research, the Army Research Office, and the National Security Agency, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE Research on stochastic networks has powerful driving applications in the modelling of manufacturing, telecommunications, and computer sys tems. These various applications have raised common mathematical issues of some subtlety, and a notable feature of the workshop was the way in which experts in different areas such as operations research, systems science and engineering, and applied mathematics have been attacking important problems from different viewpoints. |
Contents
a heavy | 1 |
stability performance analysis | 21 |
Stability of open multiclass queueing networks via fluid models | 71 |
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analysis Applications approximations arrival process arrival rate assume asymptotic asymptotically optimal b₁ Brownian motion buffer overflow buffer priority policy call of type compute consider constraints convergence cycle-time defined denote deterministic diffusion limits dynamic routing equations ergodic example exists exponential exponentially distributed FIFO finite fluid limit fluid model function given heavy traffic limit heuristic initial Kumar large deviation principle LBFS Lemma limit theorem linear program long-range dependence loss networks Markov chain Markov processes Mathematics matrix mean number multiclass networks multiclass queueing networks node non-idling non-negative number of customers obtain optimal control optimal policy parameters Poisson process problem proof queue length queueing systems re-entrant line satisfy scheduling policies Section semimartingale sequence server service discipline solution SRBM stability station stationary distribution stochastic stochastic networks Subsection Theorem 3.1 theory trunk reservation vector vehicles weak convergence zero μι