Time-Scaling Limits for Markov-Modulated Infinite-Server Queues

DOI10.1080/15326349.2013.750536zbMath1271.60096OpenAlexW2104171244MaRDI QIDQ4929149

H. Thorsdottir, M. R. H. Mandjes, Joke G. Blom

Publication date: 13 June 2013

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/15326349.2013.750536

zbMATH Keywords

queuesdiffusion limitMarkov-modulated Poisson process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Processes in random environments (60K37) Limit theorems in probability theory (60F99)

Related Items (9)

A functional central limit theorem for a Markov-modulated infinite-server queue ⋮ A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems ⋮ ANALYSIS OF MARKOV-MODULATED INFINITE-SERVER QUEUES IN THE CENTRAL-LIMIT REGIME ⋮ An Infinite-Server Queueing $$MMAP_k|G_k|\infty $$ Model in Semi-Markov Random Environment Subject to Catastrophes ⋮ Markov-modulated infinite-server queues with general service times ⋮ Tail asymptotics of a Markov-modulated infinite-server queue ⋮ Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit ⋮ Markov-modulated Ornstein–Uhlenbeck processes ⋮ Infinite server queues in a random fast oscillatory environment

Cites Work

• Stochastic decomposition in M/M/\({\infty}\) queues with Markov modulated service rates
• \(M/M/\infty\) queues in semi-Markovian random environment
• An infinite-server queue influenced by a semi-Markovian environment
• Stochastic-Process Limits
• Semi-Markov-Modulated Infinite-Server Queues: Approximations by Time-Scaling
• The M/M/∞ queue in a random environment

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