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 the best-possible in an asymptotically sense 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 achieve the best-possible competitive ratio in an asymptotically sense when solving the non-preemptive machine minimization problem.

中文翻译：

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智能电网模型中的非抢占式调度及其对机器最小化的影响

我们研究了智能电网需求响应管理中出现的调度问题。消费者以灵活可行的时间间隔发送电力请求，在此期间他们的请求可以得到服务。电网控制器在接收到电力请求后，在指定的时间间隔内调度每个请求。电力成本是通过每个时隙中负载的凸函数来衡量的。目标是以最小的总电力成本调度所有请求。以前的工作研究了作业具有单位功率要求和单位持续时间的情况。我们将研究扩展到任意功率要求和持续时间，这已被证明是 NP-hard。我们给出了一般问题的第一个在线算法，并证明该问题是固定参数易处理的。我们还表明，当目标是最小化峰值负载时，在线算法在渐近意义上是最好的。此外，我们观察到经典的非抢占式机器最小化问题是具有 min-peak 目标的智能电网问题的一个特例，并表明在解决非抢占式机器时，我们可以在渐近意义上实现最佳竞争比。机器最小化问题。