SELFISHMIGRATE: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online \emph{non-clairvoyant} setting. In this problem, a set of jobs $J$ arrive over time to be scheduled on a set of $M$ machines. Each job $j$ has processing length $p_j$, weight $w_j$, and is processed at a rate of $\ell_{ij}$ when scheduled on machine $i$. The online scheduler knows the values of $w_j$ and $\ell_{ij}$ upon arrival of the job, but is not aware of the quantity $p_j$. We present the {\em first} online algorithm that is {\em scalable} ((1+\eps)-speed $O(\frac{1}{\epsilon^2})$-competitive for any constant \eps > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations. We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines and obtain a scalable algorithm. The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms

Robust Online Speed Scaling With Deadline Uncertainty

A speed scaling problem is considered, where time is divided into slots, and jobs with payoff v arrive at the beginning of the slot with associated deadlines d. Each job takes one slot to be processed, and multiple jobs can be processed by the server in each slot with energy cost g(k) for processing k jobs in one slot. The payoff is accrued by the algorithm only if the job is processed by its deadline. We consider a robust version of this speed scaling problem, where a job on its arrival reveals its payoff v, however, the deadline is hidden to the online algorithm, which could potentially be chosen adversarially and known to the optimal offline algorithm. The objective is to derive a robust (to deadlines) and optimal online algorithm that achieves the best competitive ratio. We propose an algorithm (called min-LCR) and show that it is an optimal online algorithm for any convex energy cost function g(.). We do so without actually evaluating the optimal competitive ratio, and give a general proof that works for any convex g, which is rather novel. For the popular choice of energy cost function g(k) = k^alpha, alpha >= 2, we give concrete bounds on the competitive ratio of the algorithm, which ranges between 2.618 and 3 depending on the value of alpha. The best known online algorithm for the same problem, but where deadlines are revealed to the online algorithm has competitive ratio of 2 and a lower bound of sqrt{2}. Thus, importantly, lack of deadline knowledge does not make the problem degenerate, and the effect of deadline information on the optimal competitive ratio is limited

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

Advances and Technologies in High Voltage Power Systems Operation, Control, Protection and Security

The electrical demands in several countries around the world are increasing due to the huge energy requirements of prosperous economies and the human activities of modern life. In order to economically transfer electrical powers from the generation side to the demand side, these powers need to be transferred at high-voltage levels through suitable transmission systems and power substations. To this end, high-voltage transmission systems and power substations are in demand. Actually, they are at the heart of interconnected power systems, in which any faults might lead to unsuitable consequences, abnormal operation situations, security issues, and even power cuts and blackouts. In order to cope with the ever-increasing operation and control complexity and security in interconnected high-voltage power systems, new architectures, concepts, algorithms, and procedures are essential. This book aims to encourage researchers to address the technical issues and research gaps in high-voltage transmission systems and power substations in modern energy systems

Nonclairvoyantly Scheduling Power-Heterogeneous Processors

Abstract—We show that a natural nonclairvoyant online algorithm for scheduling jobs on a power-heterogeneous multiprocessor is bounded-speed bounded-competitive for the objective of flow plus energy. Keywords-Speed scaling, power management I