Energy-Efficient Flow Scheduling and Routing with Hard Deadlines in Data Center Networks

The power consumption of enormous network devices in data centers has emerged as a big concern to data center operators. Despite many traffic-engineering-based solutions, very little attention has been paid on performance-guaranteed energy saving schemes. In this paper, we propose a novel energy-saving model for data center networks by scheduling and routing "deadline-constrained flows" where the transmission of every flow has to be accomplished before a rigorous deadline, being the most critical requirement in production data center networks. Based on speed scaling and power-down energy saving strategies for network devices, we aim to explore the most energy efficient way of scheduling and routing flows on the network, as well as determining the transmission speed for every flow. We consider two general versions of the problem. For the version of only flow scheduling where routes of flows are pre-given, we show that it can be solved polynomially and we develop an optimal combinatorial algorithm for it. For the version of joint flow scheduling and routing, we prove that it is strongly NP-hard and cannot have a Fully Polynomial-Time Approximation Scheme (FPTAS) unless P=NP. Based on a relaxation and randomized rounding technique, we provide an efficient approximation algorithm which can guarantee a provable performance ratio with respect to a polynomial of the total number of flows.Comment: 11 pages, accepted by ICDCS'1

Routing versus energy optimization in a linear network

In wireless networks, devices (or nodes) often have a limited battery supply to use for the sending and reception of transmissions. By allowing nodes to relay messages for other nodes, the distance that needs to be bridged can be reduced, thus limiting the energy needed for a transmission. However, the number of transmissions a node needs to perform increases, costing more energy. Defining the lifetime of the network as the time until the first node depletes its battery, we investigate the impact of routing choices on the lifetime. In particular we focus on a linear network with nodes sending messages directly to all other nodes, or using full routing where transmissions are only sent to neighbouring nodes. We distinguish between networks with nodes on a grid or uniformly distributed and with full or random battery supply. Using simulation we validate our analytical results and discuss intermediate options for relaying of transmissions

Compact Routing on Internet-Like Graphs

The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme on random graphs with power-law node degree distributions, $P_k \sim k^{-\gamma}$. We find that the average stretch is very low and virtually independent of $\gamma$. In particular, for the Internet interdomain graph, $\gamma \sim 2.1$, the average stretch is around 1.1, with up to 70% of paths being shortest. As the network grows, the average stretch slowly decreases. The routing table is very small, too. It is well below its upper bounds, and its size is around 50 records for $10^4$-node networks. Furthermore, we find that both the average shortest path length (i.e. distance) $\bar{d}$ and width of the distance distribution $\sigma$ observed in the real Internet inter-AS graph have values that are very close to the minimums of the average stretch in the $\bar{d}$- and $\sigma$-directions. This leads us to the discovery of a unique critical quasi-stationary point of the average TZ stretch as a function of $\bar{d}$ and $\sigma$. The Internet distance distribution is located in a close neighborhood of this point. This observation suggests the analytical structure of the average stretch function may be an indirect indicator of some hidden optimization criteria influencing the Internet's interdomain topology evolution.Comment: 29 pages, 16 figure

Throughput Optimal On-Line Algorithms for Advanced Resource Reservation in Ultra High-Speed Networks

Advanced channel reservation is emerging as an important feature of ultra high-speed networks requiring the transfer of large files. Applications include scientific data transfers and database backup. In this paper, we present two new, on-line algorithms for advanced reservation, called BatchAll and BatchLim, that are guaranteed to achieve optimal throughput performance, based on multi-commodity flow arguments. Both algorithms are shown to have polynomial-time complexity and provable bounds on the maximum delay for 1+epsilon bandwidth augmented networks. The BatchLim algorithm returns the completion time of a connection immediately as a request is placed, but at the expense of a slightly looser competitive ratio than that of BatchAll. We also present a simple approach that limits the number of parallel paths used by the algorithms while provably bounding the maximum reduction factor in the transmission throughput. We show that, although the number of different paths can be exponentially large, the actual number of paths needed to approximate the flow is quite small and proportional to the number of edges in the network. Simulations for a number of topologies show that, in practice, 3 to 5 parallel paths are sufficient to achieve close to optimal performance. The performance of the competitive algorithms are also compared to a greedy benchmark, both through analysis and simulation.Comment: 9 pages, 8 figure

An Upper Bound on Multi-hop Transmission Capacity with Dynamic Routing Selection

This paper develops upper bounds on the end-to-end transmission capacity of multi-hop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the maximum diversity case. A useful aspect of the upper bound is its simple form for an arbitrary-sized network, which allows insights into how the number of hops and other network parameters affect spatial throughput in the non-asymptotic regime. The outage probability analysis is then extended to account for retransmissions with a maximum number of allowed attempts. In contrast to prevailing wisdom, we show that predetermined routing (such as nearest-neighbor) is suboptimal, since more hops are not useful once the network is interference-limited. Our results also make clear that randomness in the location of relay sets and dynamically varying channel states is helpful in obtaining higher aggregate throughput, and that dynamic route selection should be used to exploit path diversity.Comment: 14 pages, 5 figures, accepted to IEEE Transactions on Information Theory, 201

Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method

We use the incompressibility method based on Kolmogorov complexity to determine the total number of bits of routing information for almost all network topologies. In most models for routing, for almost all labeled graphs $\Theta (n^2)$ bits are necessary and sufficient for shortest path routing. By `almost all graphs' we mean the Kolmogorov random graphs which constitute a fraction of $1-1/n^c$ of all graphs on $n$ nodes, where $c > 0$ is an arbitrary fixed constant. There is a model for which the average case lower bound rises to $\Omega(n^2 \log n)$ and another model where the average case upper bound drops to $O(n \log^2 n)$. This clearly exposes the sensitivity of such bounds to the model under consideration. If paths have to be short, but need not be shortest (if the stretch factor may be larger than 1), then much less space is needed on average, even in the more demanding models. Full-information routing requires $\Theta (n^3)$ bits on average. For worst-case static networks we prove a $\Omega(n^2 \log n)$ lower bound for shortest path routing and all stretch factors $<2$ in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea

Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo