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

doi:10.1088/1674-1056/ad5d92

Abstract 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.

Keywords: kinetic theory service time Fokker-Planck equation value function

Received: 02 April 2024
Revised: 01 July 2024
Accepted manuscript online: 02 July 2024

PACS:	05.20.Dd	(Kinetic theory)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	05.10.Gg	(Stochastic analysis methods)
	47.45.Ab	(Kinetic theory of gases)

Fund: Project supported by the Special Project of Yili Normal University (to improve comprehensive strength of disciplines) (Grant No. 22XKZZ18), Yili Normal University Scientific Research Innovation Team Plan Project (Grant No. CXZK2021015), and Yili Science and Technology Planning Project (Grant No. YZ2022B036).

Corresponding Authors: Miao Liu
E-mail: lium76@163.com

Cite this article:

Minfang Zhao(赵敏芳), Lingting Kong(孔令婷), Miao Liu(刘淼), and Shaoyong Lai(赖绍永) Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions 2024 Chin. Phys. B 33 090502

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

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