Mean field for performance models with generally distributed-timed transitions

In this paper we extend the mean-field limit of a class of stochastic models with exponential and deterministic delays to include exponential and generally-distributed delays. Our main focus is the rigorous proof of the mean-field limit

Mean field for performance models with generally distributed-timed transitions

In this paper we extend the mean-field limit of a class of stochastic models with exponential and deterministic delays to include exponential and generally-distributed delays. Our main focus is the rigorous proof of the mean-field limit

Mean-field approximation of counting processes from a differential equation perspective

Deterministic limit of a class of continuous time Markov chains is considered based purely on differential equation techniques. Starting from the linear system of master equations, ordinary differential equations for the moments and a partial differential equation, called Fokker–Planck equation, for the distribution is derived. Introducing closures at the level of the second and third moments, mean-field approximations are introduced. The accuracy of the mean-field approximations and the Fokker–Planck equation is investigated by using two differential equation-based and an operator semigroup-based approach