Divisible load scheduling on arbitrary distributed networks via virtual routing approach

In this paper, we classify the dynamic, decentralized load balancing algorithms for heterogenous distributed computer systems into three policies: queue adjustment policy (QAP), rate adjustment policy (RAP) and queue and rate adjustment policy (QRAP). We propose two efficient algorithms, referred to as rate based load balancing via virtual routing (RLBVR) and queue based load balancing via virtual routing (QLBVR), which belong to the above RAP and QRAP policies, respectively. We also consider algorithms estimated load information scheduling algorithm (ELISA) that was introduced in the literature, to implement QAP policy. Our focus is to analyze and understand the behaviors of these algorithms in terms of their load balancing ability under varying load conditions (light, moderate, or high) and the minimization of mean response time of jobs. We compare the above classes of algorithms by a number of rigorous simulation experiments to elicit their behavior under some influencing parameters. From these experiments, recommendations are drawn to prescribe the suitability of the algorithms under various situations.

In this thesis, we study the theoretical approach on energy-efficient scheduling problems arising in demand response management in the modern electrical smart grid. Consumers send in power requests with flexible feasible timeslots during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. We study the smart grid scheduling problem in different models. For the offline model, we prove the problem is NP-hard for the general case. We propose a polynomial time algorithm for special input where jobs have unit power request and unit time duration. By adapting the polynomial time algorithm for unit-size jobs, we propose an approximation algorithm for more general input. On the other hand, we also present an exact algorithm to find the optimal schedule for the problem with general input. For the online model, we propose an online algorithm for jobs with jobs with arbitrary power request, arbitrary time duration, and arbitrary contiguous feasible intervals. We also show a lower bound of the competitive ratio for the smart grid scheduling problem with unit height and arbitrary width. For special cases, we design different online algorithms with better competitive ratios. Finally, we look at other optimization problems and show how to solve them by adapting our techniques. We prove that our online algorithm can solve the machine minimization problem with an asymptotically optimal competitive ratio. We also show that our exact algorithm can be adapted to solve other demand response management problems.

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed-scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.

VRP is a common problem that occurred in logistics, including determination a route of products from the source to the destination. VRPTW is variation of VRP that use routing concepts in the serving process at the certain time interval. Recently, many methods are used to solve this optimization problem, for example ACO. LTKC-ACO was developed to improve the ACO solutions that apply LTKC to obtain a number of classes that are considered as the candidate list in ACO. Local Search is also used to avoid ACO getting stuck in the local optimum. In this study, two types of LTKC-ACO are developed that’s related to time windows parameter usage in clustering. The experimental result of 56 Solomon’s datasets showed that LTKC-ACO can improve the ACO solutions on 73,21% of datasets and can out performed then the other methods, especially on the datasets that have longer scheduling of service time. Full Text: PDF DOI: http://dx.doi.org/10.11591/telkomnika.v16i2.8800

A divisible load is an amount W of computational work that can be arbitrarily divided into chunks and distributed among a set P of worker processors to be processed in parallel. Divisible load applications occur in many fields of science and engineering. They can be parallelized in a master‐worker fashion, but they pose several scheduling challenges. The divisible load scheduling problem consists in (a) selecting a subset of active workers, (b) defining the order in which the chunks will be transmitted to each of them, and (c) deciding the amount of load that will be transmitted to each worker , with , so as to minimize the makespan, i.e., the total elapsed time since the master began to send data to the first worker, until the last worker stops its computations. In this work, we propose a biased random‐key genetic algorithm for solving the divisible load scheduling problem. Computational results show that the proposed heuristic outperforms the best heuristic in the literature.

Scheduling divisible loads in distributed systems is the subject of divisible load theory (DLT). In this paper we show that coalitional game theory is a natural fit for modeling DLT as the participants in the scheduling algorithm must cooperate in order to execute a job. We devise a coalitional scheduling game in which the job owners and the independent organizations that own processors form coalitions in order to maximize their profits. We examine the payoffs to the participants and show that the core of the proposed coalitional scheduling game is non-empty. Then we examine the fair sharing of the payoffs among the participants using the Shapley value. Finally we study by simulation the properties of the proposed coalitional scheduling game considering different distributed systems configurations.

Many applications in scientific and engineering domains are structured as large numbers of independent tasks with low granularity. These applications are thus amenable to straightforward parallelization, typically in master-worker fashion, provided that efficient scheduling strategies are available. Such applications have been called divisible-loads because a scheduler may divide the computation among worker processes arbitrarily, both in terms of number of tasks and of task sizes. Divisible load scheduling has been an active area of research for the last 15 years. A vast literature offers results and scheduling algorithms for various models of the underlying distributed computing platform. Broad surveys are available that report on, accomplishments in the field. By contrast, We propose a unified theoretical perspective that synthesizes previously published results, several novel results, and open questions, in a view to foster hover divisible load scheduling research. Specifically, we discuss both one-round and multiround algorithms, and we restrict our scope to the popular star and tree network topologies, which we study with both linear and affine cost models for communication and computation.

In a distributed computing environment, guaranteeing the hard deadline for real-time messages is essential to ensure schedulability of real-time tasks. Since capabilities of the shared resources for transmission are limited, e.g., the buffer size is limited on network devices, it becomes a challenge to design an effective and feasible resource sharing policy based on both the demand of real-time packet transmissions and the limitation of resource capabilities. We address this challenge in two cooperative mechanisms. First, we design a static routing algorithm to find forwarding paths for packets to guarantee their hard deadlines. The routing algorithm employs a validation-based backtracking procedure capable of deriving the demand of a set of real-time packets on each shared network device, and it checks whether this demand can be met on the device. Second, we design a packet scheduler that runs on network devices to transmit messages according to our routing requirements. We implement these mechanisms on virtual software-defined network (SDN) switches and evaluate them on real hardware in a local cluster to demonstrate the feasibility and effectiveness of our routing algorithm and packet scheduler.

This thesis explores possibilities and limitations of extending classical combinatorial optimization problems for network flows and network design. We propose new mathematical models for logistics networks that feature commodities with multidimensional properties, e.g. their mass and volume, to capture consolidation effects of commodities with complementing properties. We provide new theoretical insights and solution methods with immediate practical impact that we test on real-world instances from the automotive, chemical, and retail industry. The first model is for tactical transportation planning with temporal consolidation effects. We propose various heuristics and prove for our instances, that most of our solutions are within a single-digit percentage of the optimum. We also study problem variants where commodities are routed unsplittably and give hardness results for various special cases and a dynamic program that finds optimal forest solutions, which overestimate real costs. The second model is for strategic route planning under uncertainty. We provide for a robust optimization method that anticipates fluctuations of demands by minimizing worst-case costs over a restricted scenario set. We show that the adversary problem is NP-hard. To still find solutions with very good worst-case cost, we derive a carefully relaxed and simplified MILP, which solves well for large instances. It can be extended to include hub decisions leading to a robust M-median hub location problem. We find a price of robustness for our instances that is moderate for scenarios using average demand values as lower bounds. Trend based scenarios show a considerable tradeoff between historical average costs and worst case costs. Another robustness concept are incremental hub chains that provide solutions for every number of hubs to operate, such that they are robust under changes of this number. A comparison of incremental solutions with M-median solutions obtained with an LP-based search suggests that a price of being incremental is low for our instances. Finally, we investigate the problem of scheduling the maintenance of edges in a network. We focus on maintaining connectivity between two nodes over time. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and for the non-preemptive case, we show strong non-approximability results.

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

An efficient assignment and scheduling of tasks of a multiprocessor program is one of the key elements in the effective utilization of multiprocessor systems. This problem being hard to solve exactly, is the reason that so many heuristic methods for finding a suboptimal schedule exist (Hou et al., 1994; Tsuchiya et al., 1997). This paper addresses the problem of multiprocessor scheduling represented as a directed acyclic task graph (DAG) without communication costs to fully connected multiprocessors. We proposed an algorithm, called PGA/SPF (Priority-based Genetic Algorithm/Shortest Processor First schedule) where a priority-based genetic algorithm is improved with the introduction of some knowledge about the scheduling problem, which is represented by the use of genetic operators as crossover and mutation operators. And, a new mapping method, shortest processor first schedule, assigns the selected task to a processor that can minimize a task execution time efficiently. The proposed algorithms generate similar or even better solutions than the previous algorithms in terms of the completion times of the resulting schedules.

Short-term power generation scheduling rules for cascade hydropower stations based on hybrid algorithm

A fundamental problem in computer and communication networks is the wavelength assignment (WA) problem: given a set of routing paths on a network, assign wavelengths (channels) to the paths such that the paths with the same wavelength are edge-disjoint. The optimization problem here is to minimize the number of wavelengths. A popular network topology is a tree of rings. It is known NP-hard to find the minimum number of wavelengths for the WA problem on a tree of rings. Let L be the maximum number of paths on any edge in the network. Then L is a lower bound on the number of wavelengths for the WA problem. We give a polynomial time algorithm which uses at most 3L wavelengths for the WA problem on a tree of rings with node degree at most eight. This improves the previous result of 4L. We also show that some instances of the WA problem require at least 3L wavelengths on a tree of rings, implying that the 3L upper bound is optimal for the worst case instances. In addition, we prove that our algorithm has approximation ratios 2 and 2.5 for a tree of rings with node degrees at most four and six, respectively.

The Network-on-Chip (NoC) is Network-version of System-on-Chip (SoC) means that on-chip communication through packet based networks. In NOC topology, routing algorithm and switching are main terminology. The routing algorithm is one of the key factors in NoC architecture. The routing algorithm which defines as the path taken by a packet between the source and the destination. The paper proposes a novel algorithm for a Network-on-Chip, which is based on packet switching. Using square mesh techniques used for 16 nodes based NoC design and simulation. The node is equal to row and column. Paper discusses internal architecture of NoC using addressable memory and simulate on XILINX 14.1 ISE MODELSIM. Keywords : Network-on-Chip, Static routing, Parallelism Cite this Article Anurag Shrivastava, Sudhir Kumar Sharma. A reliable routing architecture and algorithm for network-on-chip, Journal of Electronic Design and Technology . 2015; 6(3): 40–48p.

Compressionless Routing (GR) is a new adaptive routing framework which provides a unified framework for efficient deadlock-free adaptive routing and fault-tolerance. CR exploits the tight-coupling between wormhole routers for flow control to detect potential deadlock situations and recover from them. Fault-tolerant Compressionless Routing (FCR) extends Compressionless Routing to support end-to-end fault-tolerant delivery. Detailed routing algorithms, implementation complexity and performance simulation results for CR and FCR are presented.CR has the following advantages: deadlock-free adaptive routing in torus networks with no virtual channels, simple router designs, order-preserving message transmission, applicability to a wide variety of network topologies, and elimination of the need for buffer allocation messages. FCR has the following advantages: tolerates transient faults while maintaining data integrity (nonstop fault-tolerance), tolerates permanent faults, can be applied to a wide variety of network topologies, and eliminates the need for software buffering and retry for reliability. These advantages of CR and FCR not only simplify hardware support for adaptive routing and fault-tolerance, they also can simplify communication software layers.