Energy-Efficient Scheduling for Homogeneous Multiprocessor Systems

We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a discrete speed set, we propose solving a tractable linear program. Our formulations are based on a fluid model and a global scheduling scheme, i.e. tasks are allowed to migrate between processors. The new methods are compared with three global energy/feasibility optimal workload allocation formulations. Simulation results illustrate that our methods achieve both feasibility and energy optimality and outperform existing methods for constrained deadline tasksets. Specifically, the results provided by our algorithm can achieve up to an 80% saving compared to an algorithm without a frequency scaling scheme and up to 70% saving compared to a constant frequency scaling scheme for some simulated tasksets. Another benefit is that our algorithms can solve the scheduling problem in one step instead of using a recursive scheme. Moreover, our formulations can solve a more general class of scheduling problems, i.e. any periodic real-time taskset with arbitrary deadline. Lastly, our algorithms can be applied to both online and offline scheduling schemes.Comment: Corrected typos: definition of J_i in Section 2.1; (3b)-(3c); definition of \Phi_A and \Phi_D in paragraph after (6b). Previous equations were correct only for special case of p_i=d_

Energy-efficient scheduling for homogeneous multiprocessor systems

We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a discrete speed set, we propose solving a tractable linear program. Our formulations are based on a fluid model and a global scheduling scheme, i.e. tasks are allowed to migrate between processors. The new methods are compared with three global energy/feasibility optimal workload allocation formulations. Simulation results illustrate that our methods achieve both feasibility and energy optimality and outperform existing methods for constrained deadline tasksets. Specifically, the results provided by our algorithm can achieve up to an 80% saving compared to an algorithm without a frequency scaling scheme and up to 70% saving compared to a constant frequency scaling scheme for some simulated tasksets. Another benefit is that our algorithms can solve the scheduling problem in one step instead of using a recursive scheme. Moreover, our formulations can solve a more general class of scheduling problems, i.e. any periodic real-time taskset with arbitrary deadline. Lastly, our algorithms can be applied to both online and offline scheduling schemes

The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable

While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010

A Survey On Multi Trip Vehicle Routing Problem

The vehicle routing problem (VRP) and its variants are well known and greatly explored in the transportation literature. The vehicle routing problem can be considered as the scheduling of vehicles (trucks) to a set of customers under various side constraints. In most studies, a fundamental assumption is that a vehicle dispatched for service finishes its duty in that scheduling period after it returns back to the depot. Clearly, in many cases this assumption may not hold. Thus, in the last decade some studies appeared in the literature where this basic assumption is relaxed, and it is allowed for a vehicle to make multiple trips per period. We consider this new variant of the VRP an important one with direct practical impact. In this survey, we define the vehicle routing problem with multiple trips, define the current state-of-the-art, and report existing results from the current literature