Commuting Matrices in the Queue Length and Sojourn Time Analysis of MAP/MAP/1 Queues

DOI10.1080/15326349.2014.930669zbMath1318.68061OpenAlexW1969737810MaRDI QIDQ2937475

Miklós Telek, Gábor Horváth, Benny Van Houdt

Publication date: 9 January 2015

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

Full work available at URL: http://real.mtak.hu/18232/1/Commute_formal_g.pdf

zbMATH Keywords

commuting matricesqueue length distributionsojourn time distributionQBDMAP/MAP/1 queue

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (8)

Sojourn-time distribution of the \(G I/M S P/1\) queueing system ⋮ Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services ⋮ Performance analysis of work stealing strategies in large scale multi-threaded computing ⋮ Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy ⋮ Performance analysis of a \(GI/D\)-\(MSP/1/\infty\) queueing system under different service phase initiations ⋮ Strong approximations for time-varying infinite-server queues with non-renewal arrival and service processes ⋮ Queue-length, waiting-time and service batch size analysis for the discrete-time \(GI/D-MSP^{\text{(a,b)}}/1/\infty\) queueing system ⋮ Delay analysis of a queue with re-sequencing buffer and Markov environment

Cites Work

• Unnamed Item
• Analysis of a continuous time SM[K/PH[K]/1/FCFS queue: age process, sojourn times, and queue lengths]
• Sojourn time distributions in the queue defined by a general QBD process
• Age process, workload process, sojourn times, and waiting times in a discrete time SM[K/PH[K]/1/FCFS queue]
• A continuous version of matrix-analytic methods with the skip-free to the left property
• New results on the single server queue with a batch markovian arrival process
• The semi-markovian queue: theory and applications
• Markov processes whose steady state distribution is matrix-exponential with an application to the GI/PH/1 queue
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority
• The versatility of MMAP[K and the MMAP[K]/G[K]/1 queue]

This page was built for publication: Commuting Matrices in the Queue Length and Sojourn Time Analysis of MAP/MAP/1 Queues