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In this paper, the authors consider the problem of reducing network delay in stochastic network utility optimization problems. They start by studying the recently proposed Quadratic Lyapunov function based Algorithms (QLA). They show that for every stochastic problem, there is a corresponding deterministic problem, whose dual optimal solution "Exponentially attracts" the network backlog process under QLA. In particular, the probability that the backlog vector under QLA deviates from the attractor is exponentially decreasing in their Euclidean distance. This suggests that one can roughly "Subtract Out" a Lagrange multiplier from the system induced by QLA.
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