2,534 research outputs found
Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements
We consider the 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 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. 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 we relax maximum delay
constraints or throughput requirements up to constant ratios. 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 suggest a new avenue for solving maximum-delay-aware network
optimization problems. Under realistic conditions, 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. PASS is practically useful since the conditions for PASS are satisfied
in many popular application scenarios. We empirically evaluate PASS using
extensive simulations of supporting video-conferencing traffic across Amazon
EC2 datacenters. Compared to existing algorithms and a conceivable baseline,
PASS obtains up to improvement of utilities, by meeting the throughput
requirements but relaxing the maximum delay constraints that are acceptable for
practical video conferencing applications
On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Integrality Gap
We study a delay-sensitive information flow problem where a source streams
information to a sink over a directed graph G(V,E) at a fixed rate R possibly
using multiple paths to minimize the maximum end-to-end delay, denoted as the
Min-Max-Delay problem. Transmission over an edge incurs a constant delay within
the capacity. We prove that Min-Max-Delay is weakly NP-complete, and
demonstrate that it becomes strongly NP-complete if we require integer flow
solution. We propose an optimal pseudo-polynomial time algorithm for
Min-Max-Delay, with time complexity O(\log (Nd_{\max}) (N^5d_{\max}^{2.5})(\log
R+N^2d_{\max}\log(N^2d_{\max}))), where N = \max\{|V|,|E|\} and d_{\max} is the
maximum edge delay. Besides, we show that the integrality gap, which is defined
as the ratio of the maximum delay of an optimal integer flow to the maximum
delay of an optimal fractional flow, could be arbitrarily large
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