Weak stability bounds for approximations of invariant measures with applications to queueing

This paper investigate the approximation of invariant distributions for countable space Markov chains using truncations of the transition matrix. We use the weak perturbation theory to establish analytic error bounds in the GI/M/1 model and a tandem queue with blocking. Numerical examples are carrie...

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Bibliographic Details
Published in:Methodology and computing in applied probability 2020-03, Vol.22 (1), p.371-400
Main Author: Issaadi, Badredine
Format: Article
Language:English
Subjects:
Business and Management
Economics
Electrical Engineering
Error analysis
Invariants
Life Sciences
Markov chains
Mathematical models
Mathematics and Statistics
Perturbation methods
Perturbation theory
Queues
Queuing theory
Statistics
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Summary:This paper investigate the approximation of invariant distributions for countable space Markov chains using truncations of the transition matrix. We use the weak perturbation theory to establish analytic error bounds in the GI/M/1 model and a tandem queue with blocking. Numerical examples are carried out to illustrate the quality of the obtained error bounds.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-019-09708-6