Effects of Continuous vs Discrete Frequency Scaling and Core Allocation on Energy Efficiency of Static Schedules for Moldable Tasks

Models for energy-efficient static scheduling of parallelizable tasks with deadlines on frequency-scalable parallel machines comprise moldable vs. malleable tasks and continuous vs. discrete frequency levels, plus preemptive vs. non-preemptive task execution with or without task migration. We investigate the tradeoff between scheduling time and energy efficiency when going from continuous to discrete core allocation and frequency levels on a multicore processor, and from preemptive to non-preemptive task execution. To this end, we present a tool to convert a schedule computed for malleable tasks on machines with continuous frequency scaling [Sanders and Speck, Euro-Par (2012)] into one for moldable tasks on a machine with discrete frequency levels. We compare the energy efficiency of the converted schedule to the energy consumed by a schedule produced by the integrated crown scheduler [Melot et al., ACM TACO (2015)] for moldable tasks and a machine with discrete frequency levels. Our experiments with synthetic and application-based task sets indicate that the converted Sanders Speck schedules, while computed faster, consume more energy on average than crown schedules. Surprisingly, it is not the step from malleable to moldable tasks that is responsible but the step from continuous to discrete frequency levels. One-time frequency scaling during a task’s execution can compensate for most of the energy overhead caused by frequency discretization.

Hybrid Routing, Modulation, Spectrum and Core Allocation Based on Mapping Scheme

With the persistently growing popularity of internet traffic, telecom operators are forced to provide high-capacity, cost-efficient, and performance-adaptive connectivity solutions to fulfill the requirements and increase their returns. However, optical networks that make up the core of the Internet gradually reached physical transmission limits. In an attempt to provide new solutions emerged, the Space-Division Multiplexing Elastic Optical Network emerged as one of the best ways to deal with the network depletion. However, it is necessary to establish lightpaths using routing, modulation, spectrum, and core allocation (RMSCA) algorithms to establish connections in these networks. This article proposes a crosstalk-aware RMSCA algorithm that uses a multi-path and mapping scheme for improving resource allocation. The results show that the proposed algorithm decreases the blocking ratio by up to four orders of magnitude compared with other RMSCA algorithms in the literature.

The Joint Network Vehicle Routing Game

Collaborative transportation can significantly reduce transportation costs as well as greenhouse gas emissions. However, allocating the cost to the collaborating companies remains difficult. We consider the cost-allocation problem, which arises when companies, each with multiple delivery locations, collaborate by consolidating demand and combining delivery routes. We model the corresponding cost-allocation problem as a cooperative game: the joint network vehicle routing game (JNVRG). We propose a row generation algorithm to either determine a core allocation for the JNVRG or show that no such allocation exists. In this approach, we encounter a row generation subproblem, which we model as a new variant of a vehicle routing problem with profits. Moreover, we propose two main acceleration strategies for the row generation algorithm. First, we generate rows by relaxing the row generation subproblem, exploiting the tight linear programming (LP) bounds for our formulation of the row generation subproblem. Secondly, we propose to also solve the row generation subproblem heuristically and to only solve it to optimality when the heuristic fails. We demonstrate the effectiveness of the proposed row generation algorithm and the acceleration strategies by means of numerical experiments for both the JNVRG as well as the traditional vehicle routing game, which is a special case of the JNVRG. We create instances based on benchmark instances of the capacitated vehicle routing problem from the literature. We are able to either determine a core allocation or show that no core allocation exists, for instances ranging from 5 companies with a total of 79 delivery locations to 53 companies with a total of 53 delivery locations.