Computable Bounds for Conditional Steady-State Probabilities in Large Markov Chains and Queueing Models

A method is presented to compute, for the steady-state conditional probabilities of a given Markov subchain, the best lower and upper bounds derivable from the submatrix of transition probabilities between the states of that subchain only. The bounds can be improved when additional information, even...

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Bibliographic Details
Published inIEEE journal on selected areas in communications Vol. 4; no. 6; pp. 926 - 937
Main Authors Courtois, P.-J., Semal, P.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.09.1986
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Computer networks
Costs
Exact sciences and technology
Probability distribution
Queueing analysis
State-space methods
Steady-state
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Tires
Transmission and modulation (techniques and equipments)
Upper bound
Markov chain
Data transmission
Teletraffic
Models
Limit
Steady state
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Summary:A method is presented to compute, for the steady-state conditional probabilities of a given Markov subchain, the best lower and upper bounds derivable from the submatrix of transition probabilities between the states of that subchain only. The bounds can be improved when additional information, even fragmentary, on the entire chain is available. When the submatrix has a special structure, analytical expressions of the bounds can be obtained. The method is shown to be useful and economical to bound performance measures in large nonproduct-form queueing network models of computer communication systems.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.1986.1146398