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 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.