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We consider a multiple-unicast network flow problem of maximizing aggregate user utilities under link capacity constraints, maximum delay constraints, and user throughput requirements. A user's utility is a concave function of the achieved throughput or the experienced maximum delay. We first prove that it is NP-complete either (i) to construct a feasible solution meeting all constraints, or (ii) to obtain an optimal solution after we relax maximum delay constraints or throughput requirements. We then leverage a novel understanding between nonconvex maximum-delay-aware problems and their convex average-delay-aware counterparts, and design a polynomial-time approximation algorithm named PASS. PASS achieves constant or problem-dependent approximation ratios, at the cost of violating maximum delay constraints or throughput requirements by up to constant or problem-dependent ratios, under realistic conditions. We empirically evaluate our solutions using simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Compared to conceivable baselines, PASS obtains up to 100% improvement of utilities, meeting throughput requirements but relaxing maximum delay constraints that are acceptable for video conferencing applications.

Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements