From the matrix-geometric to the matrix-exponential

DOI10.1007/BF02411476zbMath0702.60084MaRDI QIDQ915281

Vaidyanathan Ramaswami

Publication date: 1990

Published in: Queueing Systems (Search for Journal in Brave)

zbMATH Keywords

time reversalmatrix-geometric methodmatrix-exponential formsMatrix-exponential steady state distributionsNeuts processstationary virtual and actual waiting

Mathematics Subject Classification ID

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

Related Items (9)

Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment ⋮ Computational methods in risk theory: a matrix-algorithmic approach ⋮ Fitting procedure for the two-state batch Markov modulated Poisson process ⋮ Sojourn time distributions in the queue defined by a general QBD process ⋮ Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis ⋮ A \(BMAP| G| 1\)-analysis based on convolution calculus ⋮ Ladder heights and the Markov-modulated M/G/1 queue ⋮ Markov-modulated PH/G/1 queueing systems ⋮ First passage times for Markov renewal processes and applications

Cites Work

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• Markov-modulated queueing systems
• The busy period of queues which have a matrix-geometric steady state probability vector
• Opsearch
• A duality theorem for the matrix paradigms in queueing theory
• An experimental evaluation of the matrix-geometric method for theGI/PH/1 queue
• A single-server queue with server vacations and a class of non-renewal arrival processes
• Stationary waiting time distribution in queues with phase type service and in quasi-birth-and-death processes
• Algorithms for the multi-server queue with phase type service
• Nonlinear Matrix Equations in Applied Probability—Solution Techniques and Open Problems
• 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
• Queues Solvable without Rouché's Theorem
• Moment formulas for the Markov renewal branching process
• Markov chains with applications in queueing theory, which have a matrix-geometric invariant probability vector
• Probabilistic interpretations of some duality results for the matrix paradigms in queueing theory

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