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This paper considers the problem of minimizing the time average of astochastic process subject to time average constraints on other processes. Acanonical example is minimizing average power in a data network subject tomulti-user throughput constraints. Another example is a (static) convexprogram. Under a Slater condition, the drift-plus-penalty algorithm is known toprovide an $O(\epsilon)$ approximation to optimality with a convergence time of$O(1/\epsilon^2)$. This paper proves the same result with a simpler techniqueand in a more general context that does not require the Slater condition. Thispaper also emphasizes application to basic convex programs, linear programs,and distributed optimization problems.

A Simple Convergence Time Analysis of Drift-Plus-Penalty for Stochastic Optimization and Convex Programs