class of problems. The finite state space model arises in the above settings when the buffers are finite and packets arriving at a fully buffered queue are lost.

Another example arises in the modelling of a wireless local area network (WLAN). Here, each particle is a wireless node trying to access a common medium, and the state of a particle represents the aggressiveness with which a packet transmission is attempted. The nodes interact with each other via the medium access control (MAC) protocol implemented in the system. Whenever a wireless node encounters a collision due to a transmission from another node, it changes its state to a less aggressive one, and whenever it succeeds, it changes its state to a more aggressive one. Therefore, the evolution of the state of a node depends on the empirical measure of the states of all the nodes, as in our mean-field model. This model was first proposed by Bianchi [@bianchi-98] and has proved to be very successful in analysing the performance of the MAC protocol; other works that focus on the WLAN application include: Bordenave et al. [@bordenave-etal-12] who studied a two time scale mean-field interacting particle system with a fast varying background 