State of the Art—Networks of Queues: A Survey of Weak Convergence Results

DOI10.1287/mnsc.24.11.1175zbMath0396.60088OpenAlexW1967003314MaRDI QIDQ4179649

Austin J. Lemoine

Publication date: 1978

Published in: Management Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1287/mnsc.24.11.1175

zbMATH Keywords

Brownian MotionWeak ConvergenceDiffusion ApproximationHeavy Traffic ApproximationQueues in TandemRepairman Problem

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (20)

A nonzero-sum risk-sensitive stochastic differential game in the orthant ⋮ Strong approximations for multiclass feedforward queueing networks. ⋮ A law of the iterated logarithm for the sojourn time process in queues in series ⋮ Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic ⋮ Weak convergence in multiphase queues ⋮ Asymptotic analysis of queueingnetworks ⋮ Brownian models of open queueing networks with homogeneous customer populations^∗ ⋮ Weak Convergence Limits for Sojourn Times in Cyclic Queues Under Heavy Traffic Conditions ⋮ Mathematical theory of queueing networks ⋮ Heavy Traffic queues with heterogeneous servers:pathwise average cost per unit time problem ⋮ Unnamed Item ⋮ Jackson network in a random environment: strong approximation ⋮ Nearly optimal control of queues in heavy traffic with heterogeneous servers ⋮ Unnamed Item ⋮ Dynamic scheduling in manufacturing systems using Brownian approximations ⋮ Diffusion approximations and nearly optimal maintenance policies for system breakdown and repair problems ⋮ Zero-sum risk-sensitive stochastic differential games with reflecting diffusions in the orthant ⋮ Theory of queuing networks and its applications to the analysis of information-computing systems ⋮ Ergodic risk-sensitive stochastic differential games with reflecting diffusions in a bounded domain ⋮ On the law of the iterated logarithm in multiserver open queueing networks

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