The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size

A Nonlinear Integral Operator Encountered in the Bandwidth Sharing of a Star-Shaped Network

We consider a symmetrical star-shaped network, in which bandwidth is shared among the active connections according to the iminj policy. Starting from a chaos propagation hypothesis, valid when the system is large enough, one can write equilibrium equations for an arbitrary link of the network. This paper describes an approach based on functional analysis of nonlinear integral operators, which allows to characterize quantitatively the behaviour of the network under heavy load conditions