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Register a new userNetwork Utility Maximization under Maximum Delay Constraints and Throughput Requirements
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Qingyu Liu
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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 users 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 $100%$ improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints that are acceptable for practical video conferencing applications.
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We consider the scenario where a sender periodically sends a batch of data to a receiver over a multi-hop network, possibly using multiple paths. Our objective is to minimize peak/average Age-of-Information (AoI) subject to throughput requirements. The consideration of batch generation and multi-path communication differentiates our AoI study from existing ones. We first show that our AoI minimization problems are NP-hard, but only in the weak sense, as we develop an optimal algorithm with a pseudo-polynomial time complexity. We then prove that minimizing AoI and minimizing maximum delay are roughly equivalent, in the sense that any optimal solution of the latter is an approximate solution of the former with bounded optimality loss. We leverage this understanding to design a general approximation framework for our problems. It can build upon any $alpha$-approximation algorithm of the maximum delay minimization problem, to construct an $(alpha+c)$-approximate solution for minimizing AoI. Here $c$ is a constant depending on the throughput requirements. Simulations over various network topologies validate the effectiveness of our approach.
Motivated by damage due to heating in sensor operation, we consider the throughput optimal offline data scheduling problem in an energy harvesting transmitter such that the resulting temperature increase remains below a critical level. We model the temperature dynamics of the transmitter as a linear system and determine the optimal transmit power policy under such temperature constraints as well as energy harvesting constraints over an AWGN channel. We first derive the structural properties of the solution for the general case with multiple energy arrivals. We show that the optimal power policy is piecewise monotone decreasing with possible jumps at the energy harvesting instants. We derive analytical expressions for the optimal solution in the single energy arrival case. We show that, in the single energy arrival case, the optimal power is monotone decreasing, the resulting temperature is monotone increasing, and both remain constant after the temperature hits the critical level. We then generalize the solution for the multiple energy arrival case.
We consider the Network Utility Maximization (NUM) problem for wireless networks in the presence of arbitrary types of flows, including unicast, broadcast, multicast, and anycast traffic. Building upon the recent framework of a universal control policy (UMW), we design a utility optimal cross-layer admission control, routing and scheduling policy, called UMW+. The UMW+ policy takes packet level actions based on a precedence-relaxed virtual network. Using Lyapunov optimization techniques, we show that UMW+ maximizes network utility, while simultaneously keeping the physical queues in the network stable. Extensive simulation results validate the performance of UMW+; demonstrating both optimal utility performance and bounded average queue occupancy. Moreover, we establish a precise one-to-one correspondence between the dynamics of the virtual queues under the UMW+ policy, and the dynamics of the dual variables of an associated offline NUM program, under a subgradient algorithm. This correspondence sheds further insight into our understanding of UMW+.
In this paper, we present two completely uncoupled algorithms for utility maximization. In the first part, we present an algorithm that can be applied for general non-concave utilities. We show that this algorithm induces a perturbed (by $epsilon$) Markov chain, whose stochastically stable states are the set of actions that maximize the sum utility. In the second part, we present an approximate sub-gradient algorithm for concave utilities which is considerably faster and requires lesser memory. We study the performance of the sub-gradient algorithm for decreasing and fixed step sizes. We show that, for decreasing step sizes, the Cesaro averages of the utilities converges to a neighbourhood of the optimal sum utility. For constant step size, we show that the time average utility converges to a neighbourhood of the optimal sum utility. Our main contribution is the expansion of the achievable rate region, which has been not considered in the prior literature on completely uncoupled algorithms for utility maximization. This expansion aids in allocating a fair share of resources to the nodes which is important in applications like channel selection, user association and power control.
Due to the presence of buffers in the inner network nodes, each congestion event leads to buffer queueing and thus to an increasing end-to-end delay. In the case of delay sensitive applications, a large delay might not be acceptable and a solution to properly manage congestion events while maintaining a low end-to-end delay is required. Delay-based congestion algorithms are a viable solution as they target to limit the experienced end-to-end delay. Unfortunately, they do not perform well when sharing the bandwidth with congestion control algorithms not regulated by delay constraints (e.g., loss-based algorithms). Our target is to fill this gap, proposing a novel congestion control algorithm for delay-constrained communication over best effort packet switched networks. The proposed algorithm is able to maintain a bounded queueing delay when competing with other delay-based flows, and avoid starvation when competing with loss-based flows. We adopt the well-known price-based distributed mechanism as congestion control, but: 1) we introduce a novel non-linear mapping between the experienced delay and the price function and 2) we combine both delay and loss information into a single price term based on packet interarrival measurements. We then provide a stability analysis for our novel algorithm and we show its performance in the simulation results carried out in the NS3 framework. Simulation results demonstrate that the proposed algorithm is able to: achieve good intra-protocol fairness properties, control efficiently the end-to-end delay, and finally, protect the flow from starvation when other flows cause the queuing delay to grow excessively.
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