A biologically inspired fluid model of the cyclic service system

A deterministic fluid model in the form of nonlinear ordinary differential equations is developed to provide the description for a multichannel service system with service-in-random-order queue discipline, abandonment and re-entry, where servers are treated like enzyme molecules. The parametric analys...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 25; no. 4; pp. 505 - 521
Main Authors Kantarbayeva, Aliya, Mustafin, Almaz
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 13.10.2020
Subjects
abandonment
clearing function
Commodities
Differential equations
Enzymes
multiple server
Operations research
Parametric analysis
Production functions
Production planning
random order service
re-entry
fluid queues
re-entry
random order service
clearing function
fluid queues
abandonment
multiple server
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Summary:A deterministic fluid model in the form of nonlinear ordinary differential equations is developed to provide the description for a multichannel service system with service-in-random-order queue discipline, abandonment and re-entry, where servers are treated like enzyme molecules. The parametric analysis of the model’s fixed point is given, particularly, how the arrival rate of new customers affects the steady-state demand. It is also shown that the model implies a saturating clearing function (yield vs. demand) of the Karmarkar type providing the mean service time is much shorter than the characteristic waiting time.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.10801