Mean-Field Methods in Large Stochastic Networks

Analysis of large-scale communication networks (e.g. ad hoc wireless networks, cloud computing systems, server networks etc.) is of great practical interest. The massive size of such networks frequently makes direct analysis intractable. Asymptotic approximations using fluid and diffusion scaling limits provide useful methods for approaching such problems. In this dissertation, I study such approximations in two different settings. In the first, I consider a rate control problem for a weakly interacting particle system. I show that by considering an associated diffusion control problem, one can construct controls which are asymptotically optimal for the finite particle system control problem. In the second, I consider a class of load balancing mechanisms in a large cloud-storage network that uses a Maximum Distance Separable coding scheme to store a large set of files. Fluid and diffusion approximations are developed for this system and the long-time behavior of the network is studied.Doctor of Philosoph