Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

The distribution of continuous service time in call centers is investigated. A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time, respectively. Using the statistical mechanical and asymptotic...

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Bibliographic Details
Published inChinese physics B Vol. 33; no. 9; pp. 90502 - 347
Main Authors Zhao, Minfang, Kong, Lingting, Liu, Miao, Lai, Shaoyong
Format Journal Article
LanguageEnglish
Published Chinese Physical Society and IOP Publishing Ltd 01.08.2024
Subjects
Fokker-Planck equation
kinetic theory
service time
value function
value function
Fokker-Planck equation
kinetic theory
service time
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ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/ad5d92

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Summary:The distribution of continuous service time in call centers is investigated. A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time, respectively. Using the statistical mechanical and asymptotic limit methods, Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels. The steady-state solutions of the Fokker–Planck equation are obtained in exact form. Numerical experiments are provided to support our results under different parameters.
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/ad5d92