process to model partial interference among nodes, Kumar et al. [@kumar-etal-06] who used the mean-field model to study the performance of WLANs using a fixed-point analysis, Ramaiyan et al. [@ramaiyan-etal-08] and Bhattacharya and Kumar [@bhattacharya-kumar-17] who looked at the problem of short term unfairness using the aforementioned fixed-point analysis, etc. Note that our model is a continuous-time modification of the discrete-time models in the above papers. Yet the continuous time model provides accurate predictions on the discrete-time model; see [[@borkar-sundaresan-12 page 4]]{}. For a continuous-time model, see Boorstyn et al. [@boorstyn-etal-87].

Other applications that use the mean-field model include analysis and control of spread of epidemics in networks [@benaim-leboudec-08; @akhil-etal-19; @leonard-90; @djehiche-kaj-95], dynamic routing in circuit-switched networks [@anantharam-91], scheduling in cellular systems [@manjerkar-etal-14], game-theoretic modelling and analysis of behaviour of agents in societal networks [@reiffers-sundaresan; @li-etal-15], etc.

Large deviations over finite time durations {#section:ldp_finite}
===========================================

In this section, we present a large deviation principle for the process $\mu_N$ over finite time durations. This result will be used later to study the large-time behaviour of $\mu_N$ and the rate of convergence of $\mu_N$ to its invariant measure.

Fix $T>0$. We introduce some notations. Let $p_{\nu_N}^{(N)}$ denote the solution to the $D([0,T], 