Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements
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We consider a multiple-unicast network flow problem of maximizing aggregate user utilities over a multi-hop network, subject to link capacity constraints, maximum end-to-end delay constraints, and user throughput requirements. A user's utility is an arbitrary function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia or Cyber-Physical System (CPS) traffic, and it is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. We first show that it is NP-complete to even construct a feasible solution to our problem. We then develop the first set of polynomial-time algorithms in the literature, to our best knowledge, named PASS, to obtain solutions that (i) achieve constant or problem-dependent approximation ratios, at the cost of (ii) violating maximum delay constraints or throughput requirements up to constant or problem-dependent ratios, under certain conditions derived in this paper. We observe that the conditions are satisfied in many popular application scenarios, where hence PASS can be applied with strong theoretical performance guarantee. We evaluate the empirical performance of PASS in simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Our design leverages a novel understanding between non-convex maximum-delay-aware problems and their convex average-delay-aware counterparts, which can be of independent interest and suggest a new avenue for solving maximum-delay-aware network optimization problems.
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