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Elena Yudovina is a mathematician whose work includes the theory of stochastic networks. With Frank Kelly, she wrote Stochastic Networks by Frank Kelly and Elena Yudovina, connecting queueing theory, loss networks, congestion control and distributed optimization. The author's book page verifies the joint authorship and 2014 publication.^[ref]

A central question is how local service or routing rules affect an entire network. The book's M/M/1 queue illustrates the danger of operating near capacity: with arrival rate $\lambda$, service rate $\mu$ and $\rho =\lambda /\mu <1$, mean queue population is $\rho /(1-\rho )$. Modest changes in load can therefore cause large changes in delay.^[ref]

Frank Kelly works on probability theory, stochastic networks and the mathematical organization of shared resources. His research connects queueing theory with optimization: local decisions about service, admission or price can determine a network's aggregate performance. His institutional research record describes these interests.^[ref]

With Elena Yudovina, Kelly wrote Stochastic Networks by Frank Kelly and Elena Yudovina. Its treatment of loss networks shows how detailed balance can produce an explicit equilibrium occupancy law, while congestion control uses resource prices to coordinate competing demands. These are complementary uses of mathematics: predicting congestion and designing rules that improve it.^[ref]