Martingale relations for the M/GI/1 queue with Markov modulated Poisson input

DOI10.1016/0304-4149(91)90074-MzbMath0734.60092MaRDI QIDQ811026

Armand M. Makowski, François Baccelli

Publication date: 1991

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

stability conditionexponential martingalesabsolute continuity propertiessingle server queueing systemstationary behaviors of the system

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items

Exponential bounds for queues with Markovian arrivals ⋮ The MacLaurin expansion for a \(G/G/1\) queue with Markov-modulated arrivals and services ⋮ Martingale methods for analyzing the \(M|_{M}|1\) retrial queue with negative arrivals ⋮ The derivation of the Laplace transform of a wet period in a finite dam via martingales

Cites Work

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• Theory of continuous storage with Markov additive inputs and a general release rule
• Stability and bounds for single server queues in random environment
• Stochastic theory of a fluid model of producers and consumers coupled by a buffer
• The M/M/1 Queue in a Markovian Environment