Algebraic Graph Theory: The multiplicative expansion

In the past few years, with the rapid development of heterogeneous computing systems (HCS), the issue of energy consumption has attracted a great deal of attention. How to reduce energy consumption is currently a critical issue in designing HCS. In response to this challenge, many energy-aware scheduling algorithms have been developed primarily using the dynamic voltage-frequency scaling (DVFS) capability which has been incorporated into recent commodity processors. However, these techniques are unsatisfactory in minimizing both schedule length and energy consumption. Furthermore, most algorithms schedule tasks according to their average-case execution times and do not consider task execution times with probability distributions in the real-world. In realizing this, we study the problem of scheduling a bag-of-tasks (BoT) application, made of a collection of independent stochastic tasks with normal distributions of task execution times, on a heterogeneous platform with deadline and energy consumption budget constraints. We build execution time and energy consumption models for stochastic tasks on a single processor. We derive the expected value and variance of schedule length on HCS by Clark's equations. We formulate our stochastic task scheduling problem as a linear programming problem, in which we maximize the weighted probability of combined schedule length and energy consumption metric under deadline and energy consumption budget constraints. We propose a heuristic energy-aware stochastic task scheduling algorithm called ESTS to solve this problem. Our algorithm can achieve high scheduling performance for BoT applications with low time complexity $O(n(M+\log n))$ , where $n$ is the number of tasks and $M$ is the total number of processor frequencies. Our extensive simulations for performance evaluation based on randomly generated stochastic applications and real-world applications clearly demonstrate that our proposed heuristic algorithm can improve the weighted probability that both the deadline and the energy consumption budget constraints can be met, and has the capability of balancing between schedule length and energy consumption.

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Energy-Efficient Stochastic Task Scheduling on Heterogeneous Computing Systems

Mobile Edge Computing (MEC) is considered an essential future service for the implementation of 5G networks and the Internet of Things, as it is the best method of delivering computation and communication resources to mobile devices. It is based on the connection of the users to servers located on the edge of the network, which is especially relevant for real-time applications that demand minimal latency. In order to guarantee a resource-efficient MEC (which, for example, could mean improved Quality of Service for users or lower costs for service providers), it is important to consider certain aspects of the service model, such as where to offload the tasks generated by the devices, how many resources to allocate to each user (specially in the wired or wireless device-server communication) and how to handle inter-server communication. However, in the MEC scenarios with many and varied users, servers and applications, these problems are characterized by parameters with exceedingly high levels of dimensionality, resulting in too much data to be processed and complicating the task of finding efficient configurations. This will be particularly troublesome when 5G networks and Internet of Things roll out, with their massive amounts of devices. To address this concern, the best solution is to utilize Machine Learning (ML) algorithms, which enable the computer to draw conclusions and make predictions based on existing data without human supervision, leading to quick near-optimal solutions even in problems with high dimensionality. Indeed, in scenarios with too much data and too many parameters, ML algorithms are often the only feasible alternative. In this paper, a comprehensive survey on the use of ML in MEC systems is provided, offering an insight into the current progress of this research area. Furthermore, helpful guidance is supplied by pointing out which MEC challenges can be solved by ML solutions, what are the current trending algorithms in frontier ML research and how they could be used in MEC. These pieces of information should prove fundamental in encouraging future research that combines ML and MEC.

Machine Learning Meets Computation and Communication Control in Evolving Edge and Cloud: Challenges and Future Perspective

Towards energy-efficient scheduling for real-time tasks under uncertain cloud computing environment

With the continuous scaling of CMOS devices, the increase in power density and system integration level have not only resulted in huge energy consumption but also led to elevated chip temperature. Thus, energy efficient task scheduling with thermal consideration has become a pressing research issue in computing systems, especially for real-time embedded systems with limited cooling techniques. In this paper, we design a two-stage energy-efficient temperature-aware task scheduling scheme for heterogeneous real-time multiprocessor system-on-chip (MPSoC) systems. In the first stage, we analyze the energy optimality of assigning real-time tasks to multiple processors of an MPSoC system, and design a task assignment heuristic that minimizes the system dynamic energy consumption under the constraint of task deadlines. In the second stage, the optimality of minimizing the peak temperature of a processor is investigated, and a slack distribution heuristic is proposed to improve the temperature profile of each processor under the thermal constraint, thus the temperature-dependent system leakage energy consumption is reduced. Through the extensive efforts made in two stages, the system overall energy consumption is minimized. Experimental results have demonstrated the effectiveness of our scheme.

Thermal-Aware Task Scheduling for Energy Minimization in Heterogeneous Real-Time MPSoC Systems

Cloud providers offer computing services based on user demands using the Infrastructure as a Service (IaaS) service model. In a cloud data center, it is possible that multiple Virtual Machines (VMs) run on a Physical Machine (PM) using virtualization technology. Virtual Machine Placement (VMP) problem is the mapping of virtual machines across multiple physical ones. This process plays a vital role in defining energy consumption and resource usage efficiency in the cloud data center infrastructure. However, providing an efficient solution is not trivial due to difficulties such as machine heterogeneity, multi-dimensional resources, and large scale cloud data centers. In this paper, we propose an efficient heuristic algorithm that focuses on power consumption and resource wastage optimization to solve the aforementioned problem. The proposed algorithm, called MinPR, minimizes the total power consumption by reducing the number of active physical machines and prioritizing the power-efficient ones. Also, it reduces resource wastage by maximizing and balancing resource utilization among physical machines. To achieve these goals, we propose a new Resource Usage Factor model that manages virtual machine placement on physical machines using reward and penalty mechanisms. Simulations based on cloud user-customized VMs and Amazon EC2 Instances workloads illustrate that the proposed algorithm outperforms existing approaches. In particular, the proposed algorithm reduces total energy consumption by up to 15% for cloud user-customized VMs and by up to 10% for Amazon EC2 Instances.

An energy-efficient algorithm for virtual machine placement optimization in cloud data centers

Heterogeneous multiprocessors have been widely used in modern computational systems to increase the computing capability. As the performance increases, the energy consumption in these systems also increases significantly. Dynamic Voltage and Frequency Scaling (DVFS) is considered an efficient scheme to achieve the goal of saving energy, because it allows processors to dynamically adjust their supply voltages and/or execution frequencies to work on different power/energy levels. In this paper, we consider scheduling non-preemptive frame-based tasks on DVFS-enabled heterogeneous multiprocessor platforms with the goal of achieving minimal overall energy consumption. We consider three types of heterogeneous platforms, namely, dependent platforms without runtime adjusting, dependent platforms with runtime adjusting, and independent platforms. For these three platforms, we first formulate the problems as binary integer programming problems, and then, relax them as convex optimization problems, which can be solved by the well-known interior point method. We propose a Relaxation-based Iterative Rounding Algorithm (RIRA), which tries to achieve the task set partition, that is closest to the optimal solution of the relaxed problems, in every step of a task-to-processor assignment. Experiments and comparisons show that our RIRA produces a better performance than existing methods and a simple but naive method, and achieves near-optimal scheduling under most cases. We also provide comprehensive complexity, accuracy and scalability analysis for the RIRA approach by investigating the interior-point method and by running specially designed experiments. Experimental results also show that the proposed RIRA approach is an efficient and practically applicable scheme with reasonable complexity.

Minimizing Energy Consumption for Frame-Based Tasks on Heterogeneous Multiprocessor Platforms

Modern computational systems have adopted heterogeneous multiprocessors to increase their computation capability. As the performance increases, the energy consumption in these systems also increases significantly. Dynamic Voltage and Frequency Scaling (DVFS), which allows processors to dynamically adjust their supply voltages and execution frequencies to work on different power/energy levels, is considered an efficient scheme to achieve the goal of saving energy. In this paper, we consider scheduling frame-based tasks on DVFS-enabled heterogeneous multiprocessor platforms with the goal of achieving minimal overall energy consumption. We consider three types of heterogeneous platforms, namely, dependent platforms without runtime adjusting, dependent platforms with runtime adjusting, and independent platforms. For all of these three platforms, we first introduce a Relaxation-based Naive Rounding Algorithm (RNRA), which can produce good solutions for some cases, but may be unstable under other situations. Then, we propose a Relaxation-based Iterative Rounding Algorithm (RIRA). Experiments and comparisons show that our RIRA produces a better performance than RNRA and other existing methods, and achieves near-optimal scheduling under most cases.

Energy-Aware Scheduling for Frame-Based Tasks on Heterogeneous Multiprocessor Platforms

During the past decade, various novel data center network (DCN) architectures have been proposed to meet various requirements of large scale data centers. In existing works that consider server-centric DCN architectures, the lengths of a server-to-server-direct hop and a server-to-server-via-a-switch hop are assumed to be equal. We propose the concept of Normalized Switch Delay (NSD) to distinguish a server-to-server-direct hop and a server-to-server-via-a-switch hop, to unify the design and analysis of server-centric DCN architectures for interconnecting servers with two network interface cards. In [1] , the authors claim that BCN is the largest known architecture to interconnect dual-port servers, with diameter 7, given a switch port number. We notice that the existing DPillar [2] architecture accommodates more servers than BCN does under the same configurations. Motivated by this fact, we consider a fundamental problem: maximizing the number of dual-port servers, given network diameter and switch port number; and give an upper bound on this maximum number. Then, we propose three novel architectures that try to achieve this upper bound: SWCube, SWKautz, and SWdBruijn, based on the generalized hypercube, Kautz graph, and de Bruijn graph, respectively. The number of servers that SWCube can accommodate is comparable to that of DPillar. The number of servers that SWKautz and SWdBruijn can accommodate is generally greater than that of DPillar. Compared with three existing architectures, the three proposed architectures, SWCube, SWKautz and SWdBruijn demonstrate various advantages. Analysis and simulations on the newly proposed architectures also show that they have nice properties for DCNs, such as low diameter, high bisection width, good fault-tolerance, and the capability of efficiently handling network congestion.

On Data Center Network Architectures for Interconnecting Dual-Port Servers

We consider the design and analysis of Data Center Network (DCN) architectures for interconnecting dual-port servers. Unlike existing works, we propose the concept of Normalized Switch Delay (NSD) to distinguish a server-to-server-direct hop and a server-to-server-via-switch hop, to unify the design of DCN architectures. We then consider a fundamental problem: maximizing the number of dual-port servers, given network diameter and switch port number; and give an upper bound on this maximum number. Two novel architectures are proposed: SWCube and SWKautz, based on the generalized hypercube and Kautz graph, respectively, which in most cases accommodate more servers than BCN [1], which was claimed to be the largest known architecture. Compared with three existing architectures, SWCube and SWKautz demonstrate various advantages. Analysis and simulations also show that SWCube and SWKautz have nice properties for DCNs, such as low diameter, good fault-tolerance, and capability of efficiently handling network congestion.

Dawei Li

Papers

An energy-efficient algorithm for virtual machine placement optimization in cloud data centers

Minimizing Energy Consumption for Frame-Based Tasks on Heterogeneous Multiprocessor Platforms

Energy-Aware Scheduling for Frame-Based Tasks on Heterogeneous Multiprocessor Platforms

On Data Center Network Architectures for Interconnecting Dual-Port Servers

On the Design and Analysis of Data Center Network Architectures for Interconnecting Dual-Port Servers