Network Utility Maximization Under Maximum Delay Constraints and Throughput Requirements

We consider a multi-path routing problem of maximizing the aggregate user utility 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 a concave function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia traffic and is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. In this paper, we first show that it is NP-complete either (i) to construct a feasible solution strictly meeting all constraints, or (ii) to obtain an optimal solution after relaxing either the maximum delay constraints or the throughput requirements. We then develop a polynomial-time approximation algorithm named PASS. The design of PASS 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 suggests a new avenue for solving maximum-delay-aware network optimization problems. We prove that PASS always obtains approximate solutions (i.e., with theoretical performance guarantees), at the cost of violating both the maximum delay constraints and the throughput requirements by up to constant ratios. We also develop two variants of PASS, named PASS-M and PASS-T, to generate approximate solutions at the cost of violating either the maximum delay constraints or the throughput requirements by up to problem-dependent ratios. We evaluate our solutions using extensive simulations on Amazon EC2 datacenters supporting video-conferencing traffic. Compared to the existing algorithms and a conceivable baseline, our solutions obtain up to 100% improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints to the extent acceptable for practical video conferencing applications.