A unified method of analysis for queues with Markovian arrivals
type: Item
instance of: scholarly article
title: A unified method of analysis for queues with Markovian arrivals
zbMATH Open document ID: 1264.90052
DOI: 10.1155/2012/831956
author: Andrzej Chydzinski
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We deal with finite-buffer queueing systems fed by a Markovian point process. This class includes the queues of type \(M/G/1/N\), \(M^X/G/1/N\), \(PH/G/1/N\), \(MMPP/G/1/N\), \(MAP/G/1/N\), and \(BMAP/G/1/N\) and is commonly used in the performance evaluation of network traffic buffering processes. Typically, such queueing systems are studied in the stationary regime using matrix-analytic methods connected with \(M/G/1\)-type Markov processes. Herein, another method for finding transient and stationary characteristics of these queues is presented. The approach is based on finding a closed-form formula for the Laplace transform of the time-dependent performance measure of interest. The method can be used for finding all basic characteristics like queue size distribution, workload distribution, loss ratio, time to buffer overflow, and so forth. To demonstrate this, several examples for different combinations of arrival processes and characteristics are presented. In addition, the most complex results are illustrated via numerical calculations based on an IP traffic parameterization.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 6173617
Wikidata QID: Q58912141
describes a project that uses: Kpc-toolbox
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/831956
OpenAlex ID: W2015683326
cites work: A storage model with self-similar input
cites work: An application of deterministic chaotic maps to model packet traffic
cites work: A multifractal wavelet model with application to network traffic
cites work: A versatile Markovian point process
cites work: Q4738768
cites work: An EM algorithm for estimation in Markov-modulated Poisson processes
cites work: Computer Performance Evaluation. Modelling Techniques and Tools
cites work: Q4692768
cites work: A stable recursion for the steady state vector in markov chains of m/g/1 type
cites work: Solving m/g/l type markov chains: recent advances and applications
cites work: Q4411081
cites work: Time to Reach Buffer Capacity in aBMAPQueue
cites work: Q3999697
cites work: Q4945342
cites work: New results on the single server queue with a batch markovian arrival process
cites work: Exact buffer overflow calculations for queues via martingales
cites work: The transient BMAP/G/l queue
cites work: The n/g/l finite capacity queue
description: scientific article; zbMATH DE number 6173617