15,111 research outputs found

    A ϕ\phi-Competitive Algorithm for Scheduling Packets with Deadlines

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    In the online packet scheduling problem with deadlines (PacketScheduling, for short), the goal is to schedule transmissions of packets that arrive over time in a network switch and need to be sent across a link. Each packet has a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can be transmitted in any time slot, so, if the system is overloaded, some packets will inevitably miss their deadlines and be dropped. In this scenario, the natural objective is to compute a transmission schedule that maximizes the total weight of packets which are successfully transmitted. The problem is inherently online, with the scheduling decisions made without the knowledge of future packet arrivals. The central problem concerning PacketScheduling, that has been a subject of intensive study since 2001, is to determine the optimal competitive ratio of online algorithms, namely the worst-case ratio between the optimum total weight of a schedule (computed by an offline algorithm) and the weight of a schedule computed by a (deterministic) online algorithm. We solve this open problem by presenting a ϕ\phi-competitive online algorithm for PacketScheduling (where ϕ1.618\phi\approx 1.618 is the golden ratio), matching the previously established lower bound.Comment: Major revision of the analysis and some other parts of the paper. Another revision will follo

    TimeTrader: Exploiting Latency Tail to Save Datacenter Energy for On-line Data-Intensive Applications

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    Datacenters running on-line, data-intensive applications (OLDIs) consume significant amounts of energy. However, reducing their energy is challenging due to their tight response time requirements. A key aspect of OLDIs is that each user query goes to all or many of the nodes in the cluster, so that the overall time budget is dictated by the tail of the replies' latency distribution; replies see latency variations both in the network and compute. Previous work proposes to achieve load-proportional energy by slowing down the computation at lower datacenter loads based directly on response times (i.e., at lower loads, the proposal exploits the average slack in the time budget provisioned for the peak load). In contrast, we propose TimeTrader to reduce energy by exploiting the latency slack in the sub- critical replies which arrive before the deadline (e.g., 80% of replies are 3-4x faster than the tail). This slack is present at all loads and subsumes the previous work's load-related slack. While the previous work shifts the leaves' response time distribution to consume the slack at lower loads, TimeTrader reshapes the distribution at all loads by slowing down individual sub-critical nodes without increasing missed deadlines. TimeTrader exploits slack in both the network and compute budgets. Further, TimeTrader leverages Earliest Deadline First scheduling to largely decouple critical requests from the queuing delays of sub- critical requests which can then be slowed down without hurting critical requests. A combination of real-system measurements and at-scale simulations shows that without adding to missed deadlines, TimeTrader saves 15-19% and 41-49% energy at 90% and 30% loading, respectively, in a datacenter with 512 nodes, whereas previous work saves 0% and 31-37%.Comment: 13 page

    Non-preemptive Scheduling in a Smart Grid Model and its Implications on Machine Minimization

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    We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem, and prove that the problem is fixed parameter tractable. We also show that the online algorithm is asymptotically optimal when the objective is to minimize the peak load. In addition, we observe that the classical non-preemptive machine minimization problem is a special case of the smart grid problem with min-peak objective, and show that we can solve the non-preemptive machine minimization problem asymptotically optimally
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