On the Convergence of Workload in Service System to Brownian Motion with Switching Variance

A modification of service system model introduced by I. Kaj and M. S. Taqqu is considered. This model describes the dynamics in time and space of various system workloads created by a set of service processes. In the model under consideration, two types of resource having its own distribution are us...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 251; no. 1; pp. 46 - 53
Main Author Garai, E. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Springer
Springer Nature B.V
Subjects
Brownian motion
Convergence
Mathematics
Mathematics and Statistics
Operators (mathematics)
Switching
Workload
Workloads
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Summary:A modification of service system model introduced by I. Kaj and M. S. Taqqu is considered. This model describes the dynamics in time and space of various system workloads created by a set of service processes. In the model under consideration, two types of resource having its own distribution are used. Such a model can be identified with the presence of two operators of the resource. At the time of the active operator failure, one can switch to another operator whose resource has distribution workloads different from the first operator. A limit theorem on the convergence of finite-dimensional distributions of the integral workload process with two types of resource to Brownian motion with switching variance is proved.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05063-x