The heavy traffic limit of a class of Markovian queueing models

DOI10.1016/0167-6377(87)90048-4zbMath0632.60065OpenAlexW2132862313MaRDI QIDQ1095501

Soren Asmussen

Publication date: 1987

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6377(87)90048-4

zbMATH Keywords

transition matrixreflected Brownian motionheavy traffic approximationheavy traffic limit theoremmatrix- geometric stationary distributiontransient and ergodic behaviour

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (8)

Diffusion approximations for open queueing networks with service interruptions ⋮ Markov-modulated \(\mathrm{M}/\mathrm{G}/1\)-type queue in heavy traffic and its application to time-sharing disciplines ⋮ Asymptotic results for a Markov-modulated risk process with stochastic investment ⋮ A heavy-traffic-limit formula for the moments of the stationary distribution in GI/G/1-type Markov chains ⋮ Heavy-traffic asymptotics for stationary GI/G/1-type Markov chains ⋮ Asymptotics and approximations of ruin probabilities for multivariate risk processes in a Markovian environment ⋮ Risk theory in a Markovian environment ⋮ Single-server queues under overdispersion in the heavy-traffic regime

Cites Work

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• Refining diffusion approximations for queues
• Conjugate processes and the simulation of ruin problems
• An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems
• An Asymptotic Analysis of a Queueing System with Markov-Modulated Arrivals
• Transient behavior of regulated Brownian motion, II: Non-zero initial conditions
• Large deviation results for time-dependent queue length distributions
• Heavy Traffic Limit Theorems for Queues: A Survey
• Planning Queueing Simulations
• Multiple channel queues in heavy traffic. II: sequences, networks, and batches

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