Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: age process, sojourn times, and queue lengths

DOI10.1007/s11424-012-9138-0zbMath1259.90022OpenAlexW2121698656MaRDI QIDQ1761393

Qi-Ming He

Publication date: 15 November 2012

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-012-9138-0

zbMATH Keywords

waiting timesqueue lengthqueueing systemsmatrix analytic methodssemi-Markov chain\(GI/M/1\) type Markov process

Mathematics Subject Classification ID

Queues and service in operations research (90B22)

Related Items

Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services ⋮ Efficient analysis of the MMAP[\(K\)/PH[\(K\)]/1 priority queue] ⋮ Fitting correlated arrival and service times and related queueing performance ⋮ Commuting Matrices in the Queue Length and Sojourn Time Analysis of MAP/MAP/1 Queues

Uses Software

• Q-MAM

Cites Work

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• Phase-type representations in random walk and queueing problems
• Markov chains with marked transitions
• Queues in DOCSIS cable modem networks
• Age process, workload process, sojourn times, and waiting times in a discrete time SM[K/PH[K]/1/FCFS queue]
• The delay distribution of a type k customer in a first-come-first-served MMAP[K/PH[K]/1 queue]
• Workload Process, Waiting Times, and Sojourn Times in a Discrete TimeMMAP[K/SM[K]/1/FCFS Queue]
• The semi-markovian queue: theory and applications
• Phase-type representations for matrix-geometric solutions
• A single-server queue with server vacations and a class of non-renewal arrival processes
• Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues
• Markov processes whose steady state distribution is matrix-exponential with an application to the GI/PH/1 queue
• The N/G/1 queue and its detailed analysis
• 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
• Representations for matrix-geometric and matrix-exponential steady-state distributions with applications to many-server queues
• The Waiting Time Distribution of a TypekCustomer in a Discrete-Time MMAP[K/PH[K]/c (c = 1, 2) Queue Using QBDs]
• Queues with marked customers
• Marked point processes as limits of Markovian arrival streams
• Queues with semi-Markovian arrivals
• Markov renewal theory
• The versatility of MMAP[K and the MMAP[K]/G[K]/1 queue]
• Queue length distribution in a FIFO single-server queue with multiple arrival streams having different service time distributions

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