Asymptotically optimal scheduling of random malleable demands in smart grid

Abstract

We study the problem of scheduling random energy demands within a fixed normalized time horizon. Each demand has to be serviced without interruption at a constant intensity, while its duration is bounded by a pair of malleability constraints. Such constraints are assumed to be characterized by an i.i.d random vector that follows a general distribution. At each time instance, the total power consumption is computed as the sum of the intensities of all demands being serviced at that moment. Our objective is to minimize both the maximum and the total convex cost of the power consumption of the grid. The problem is considered in the asymptotic regime. In this regime, the number of demands is assumed to be large, and their (random) energy requirements are inversely proportional to the number of demands. Such setting allows us to introduce a linear-time scheduling policy and shows its asymptotic optimality with respect to both cost criteria. We first study the optimization problem in the case where all demands are available a priori, i.e., before scheduling starts. Then we extend our approach for the case of demand scheduling in an arbitrary length time horizon, where the demands arrive randomly during this time interval.