中国物理B ›› 2024, Vol. 33 ›› Issue (9): 90502-090502.doi: 10.1088/1674-1056/ad5d92

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

Minfang Zhao(赵敏芳)1,2, Lingting Kong(孔令婷)3, Miao Liu(刘淼)1,2,†, and Shaoyong Lai(赖绍永)3   

  1. 1 School of Mathematics and Statistics, Yili Normal University, Yining 835000, China;
    2 Institute of Applied Mathematics, Yili Normal University, Yining 835000, China;
    3 School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
  • 收稿日期:2024-04-02 修回日期:2024-07-01 接受日期:2024-07-02 发布日期:2024-08-27
  • 通讯作者: Miao Liu E-mail:lium76@163.com
  • 基金资助:
    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).

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

Minfang Zhao(赵敏芳)1,2, Lingting Kong(孔令婷)3, Miao Liu(刘淼)1,2,†, and Shaoyong Lai(赖绍永)3   

  1. 1 School of Mathematics and Statistics, Yili Normal University, Yining 835000, China;
    2 Institute of Applied Mathematics, Yili Normal University, Yining 835000, China;
    3 School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
  • Received:2024-04-02 Revised:2024-07-01 Accepted:2024-07-02 Published:2024-08-27
  • Contact: Miao Liu E-mail:lium76@163.com
  • Supported by:
    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).

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摘要： 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.

关键词: kinetic theory, service time, Fokker-Planck equation, value function

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.

Key words: kinetic theory, service time, Fokker-Planck equation, value function

中图分类号:  (Kinetic theory)

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