the asymptotics of the second eigenvalue of the generator of the process $\mu_N$ in the reversible case. Finally, in Section \[section:conv\_global\_minimum\], we study the convergence of the empirical measure process to a global minimum of the aforementioned ‘entropy’ function when particles are injected into the system at a suitable rate.

Examples {#section:examples}
--------

The mean-field interacting particle system that we have described can be used to model many interesting phenomena that arise in various domains such as physics, engineering, biology, etc. In this section, we shall describe some applications that are relevant to communication networks and shall point to the related literature that study these applications via mean-field models. We remark that, as far as the applicability of the mean-field model is concerned, the examples and the related literature that we have mentioned below are by no means exhaustive.

The first example is load balancing in networks. We describe the simplest model, the power of two choices, studied by Mitzenmacker [@mitzhenmaker-00]. Here, each particle is a single server $M/M/1$ queue, and the state represents the number of customers waiting in the queue. In load balancing, one is interested in routing the incoming customers to an appropriate queue so as to 