This course is an introduction to the analysis and design of algorithms for stochastic networks. It covers a broad range of performance analysis tools. It shows how to abstract out networks as stochastic dynamical systems and then use tools from the fields of optimization and stochastic control in order to optimize their performance.
Mathematical background: Convex optimization, utility functions, network utility maximization, stability, feedback delays
Statistical Multiplexing and Queues: Chernoff bound, Markov chains, delay analysis in networks, Little's law
Scheduling and Capacity Region: Stochastic stability of queues, capacity of networks, Lyapunov functions (for stochastic systems), MaxWeight Algorithm
Srikant, R. and Ying, L., 2013. Communication networks: an optimization, control, and stochastic networks perspective. Cambridge University Press. (Textbook)
Kelly, Frank, and Elena Yudovina. Stochastic networks. Vol. 2. Cambridge University Press, 2014. (Reference)