Multiprocessor speed scaling for jobs with arbitrary sizes and deadlines

In this paper we study energy efficient deadline scheduling on multiprocessors in which the processors consumes power at a rate of sα when running at speeds, where α ≥ 2. The problem is to dispatch jobs to processors and determine the speed and jobs to run for each processor so as to complete all jobs by their deadlines using the minimum energy. The problem has been well studied for the single processor case. For the multiprocessor setting, constant competitive online algorithms for special cases of unit size jobs or arbitrary size jobs with agreeable deadlines have been proposed by Albers et al. (2007). A randomized algorithm has been proposed for jobs of arbitrary sizes and arbitrary deadlines by Greiner et al. (2009). We propose a deterministic online algorithm for the general setting and show that it is O(logαP)-competitive, where P is the ratio of the maximum and minimum job size

Speed Scaling for Energy Aware Processor Scheduling: Algorithms and Analysis

We present theoretical algorithmic research of processor scheduling in an energy aware environment using the mechanism of speed scaling. We have two main goals in mind. The first is the development of algorithms that allow more energy efficient utilization of resources. The second goal is to further our ability to reason abstractly about energy in computing devices by developing and understanding algorithmic models of energy management. In order to achieve these goals, we investigate three classic process scheduling problems in the setting of a speed scalable processor. Integer stretch is one of the most obvious classical scheduling objectives that has yet to be considered in the speed scaling setting. For the objective of integer stretch plus energy, we give an online scheduling algorithm that, for any input, produces a schedule with integer stretch plus energy that is competitive with the integer stretch plus energy of any schedule that finishes all jobs. Second, we consider the problem of finding the schedule, S, that minimizes some quality of service objective Q plus B times the energy used by the processor. This schedule, S, is the optimal energy trade-off schedule in the sense that: no schedule can have better quality of service given the current investment of energy used by S, and, an additional investment of one unit of energy is insufficient to improve the quality of service by more than B. When Q is fractional weighted flow, we show that the optimal energy trade-off schedule is unique and has a simple structure, thus making it easy to check the optimality of a schedule. We further show that the optimal energy trade-off schedule can be computed with a natural homotopic optimization algorithm. Lastly, we consider the speed scaling problem where the quality of service objective is deadline feasibility and the power objective is temperature. In the case of batched jobs, we give a simple algorithm to compute the optimal schedule. For general instances, we give a new online algorithm and show that it has a competitive ratio that is an order of magnitude better than the best previously known for this problem

Essays on Integer Programming in Military and Power Management Applications

This dissertation presents three essays on important problems motivated by military and power management applications. The array antenna design problem deals with optimal arrangements of substructures called subarrays. The considered class of the stochastic assignment problem addresses uncertainty of assignment weights over time. The well-studied deterministic counterpart of the problem has many applications including some classes of the weapon-target assignment. The speed scaling problem is of minimizing energy consumption of parallel processors in a data warehouse environment. We study each problem to discover its underlying structure and formulate tailored mathematical models. Exact, approximate, and heuristic solution approaches employing advanced optimization techniques are proposed. They are validated through simulations and their superiority is demonstrated through extensive computational experiments. Novelty of the developed methods and their methodological contribution to the field of Operations Research is discussed through out the dissertation