Models and algorithms for energy-efficient scheduling with immediate start of jobs

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(nlogn) time in the single-machine case and in O(n²m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution

Wind Power Persistence Characterized by Superstatistics

Mitigating climate change demands a transition towards renewable electricity generation, with wind power being a particularly promising technology. Long periods either of high or of low wind therefore essentially define the necessary amount of storage to balance the power system. While the general statistics of wind velocities have been studied extensively, persistence (waiting) time statistics of wind is far from well understood. Here, we investigate the statistics of both high- and low-wind persistence. We find heavy tails and explain them as a superposition of different wind conditions, requiring q-exponential distributions instead of exponential distributions. Persistent wind conditions are not necessarily caused by stationary atmospheric circulation patterns nor by recurring individual weather types but may emerge as a combination of multiple weather types and circulation patterns. This also leads to Fréchet instead of Gumbel extreme value statistics. Understanding wind persistence statistically and synoptically may help to ensure a reliable and economically feasible future energy system, which uses a high share of wind generation

Average rate speed scaling

Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker (Proc. IEEE Symp. Foundations of Computer Science, pp. 374-382, 1995) considered the problem where the QoS constraint is deadline feasibility and the objective is to minimize the energy used. They proposed an online speed scaling algorithm Average Rate (AVR) that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of AVR is at most (2α) α /2 if a processor running at speed s uses power s α . We show the competitive ratio of AVR is at least ((2-δ)α) α /2, where δ is a function of α that approaches zero as α approaches infinity. This shows that the competitive analysis of AVR by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of AVR is at most (2α) α /2 using a potential function argument. We believe that this analysis is significantly simpler and more elementary than the original analysis of AVR in Yao et al. (Proc. IEEE Symp. Foundations of Computer Science, pp. 374-382, 1995). © 2009 Springer Science+Business Media, LLC.link_to_subscribed_fulltex

Parity and strong parity edge-colorings of graphs

[[abstract]]A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. A parity edge-coloring (respectively, strong parity edge-coloring) is an edge-coloring in which there is no nontrivial parity path (respectively, open parity walk). The parity edge-chromatic number p(G) (respectively, strong parity edge-chromatic number pˆ(G) ) is the least number of colors in a parity edge-coloring (respectively, strong parity edge-coloring) of G. Notice that pˆ(G)≥p(G)≥χ′(G)≥Δ(G) for any graph G. In this paper, we determine pˆ(G) and p(G) for some complete bipartite graphs and some products of graphs. For instance, we determine pˆ(Km,n) and p(K m,n ) for m≤n with n≡0,−1,−2 (mod 2⌈lg m⌉).[[notice]]補正完