Scheduling Monotone Moldable Jobs in Linear Time

A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing number of allotted processors. We consider the problem of scheduling monotone moldable jobs to minimize the makespan. We argue that for certain compact input encodings a polynomial algorithm has a running time polynomial in n and log(m), where n is the number of jobs and m is the number of machines. We describe how monotony of jobs can be used to counteract the increased problem complexity that arises from compact encodings, and give tight bounds on the approximability of the problem with compact encoding: it is NP-hard to solve optimally, but admits a PTAS. The main focus of this work are efficient approximation algorithms. We describe different techniques to exploit the monotony of the jobs for better running times, and present a (3/2+{\epsilon})-approximate algorithm whose running time is polynomial in log(m) and 1/{\epsilon}, and only linear in the number n of jobs

Piece-wise scheduling of composite task graphs onto distributed memory parallel computers

Heuristics for static scheduling of task graphs using list scheduling techniques have continued to improve by adding real-world factors such as processor speed, network transmission speed, interconnection topology, and link contention considerations to the basic task graph model. Yet, the resulting schedules do not fully model program loops and branches, startup costs for both process creation and message initiation, and a number of interesting parallel processing patterns such as meshes, tress, and supervisor/workers. In fact, improvements in the schedule may be obtained when the task graph is regular as when it contains repeated or replicated tasks, divide-and-conquer patterns of communication, or a mesh-structured pattern of computation. In this paper we describe a limited approach to scheduling composite task graphs that considers process and message startup costs, and three regular patterns : replicated, tree, and mesh. The approach is to model programs with such regular patterns as a composite task graph, where each regular structure is a decomposable sub-task node in the task graph. Then, we compute an optimal schedule for each sub-task. graph, piece the sub-tasks together, and perform an ordinary static scheduling heuristic on the pieces, to produce an overall schedule. We define a composite task graph as a hierarchical task graph containing regular-structured sub-task graphs as components. At the top level of this hierarchy, each graph node represents either a simple task or a hierarchically decomposable sub-task graph. We propose a piece-wise scheduling algorithm that simply allocates processors to sub-task graphs according to closed-form expressions which give determine the optimal number of processors, and then uses a list scheduling algorithm to schedule the flattened graph onto these processors. We do not address the pressing problem of loops and branches in the task graph representation, but we speculate that the technique of piece-wise scheduling introduced here can be adapted to a hybrid form of scheduling that may accommodate branches and loops. Piece-wise scheduling is not guaranteed to yield the best global schedule. Rather, it pieces together locally optimum sub-schedules. Finding globally optimum schedules for composite task graphs remains an open problem. We present an heuristic approach that has been experimentally used to schedule small parallel programs with encouraging results. More empirical evidence is needed to determine the usefulness of this technique, but early indications are encouraging

Space sharing job scheduling policies for parallel computers

The distinguishing characteristic of space sharing parallel job scheduling policies is that applications are allocated non-overlapping processor subsets. The interference among jobs is reduced, the synchronization delays and message latencies can be predictable, and distinct processors may be allocated to cooperating processes so as to avoid the overhead of context switches associated with traditional time-multiplexing;The processor allocation strategy, the job selection criteria, and workload characteristics are fundamental factors that influence system performance under space sharing. Allocation can be static or dynamic. The processor subset allocated to an application is fixed under static space sharing, whereas it can change during execution under dynamic space sharing. Static allocation can produce more predictable run times, permits a wide range of compiler optimizations (e.g., static data distribution and binding), and avoids the processor releases and reallocations associated with dynamic allocation. Its major problem is that it can induce high processor fragmentation;In this dissertation, alternative static and dynamic space sharing policies that differ in the allocation discipline and the job selection criteria are studied. The results show that significantly superior performance can be achieved under static space sharing if applications can be folded (i.e., allocated fewer processors than they requested). Folding typically increases program efficiency and can reduce processor fragmentation. Policies that increase folding with the system load are proposed and compared to schemes that use unconstrained folding, no folding, and fixed maximum folding factors. The adaptive policies produced higher and more stable system utilization, significantly shorter mean response times, and good fairness curves. However, unconstrained folding resulted in considerably more severe processor fragmentation than no folding. Its advantage is that it exploits the efficiency improvement that typically results when an application is allocated fewer processors. Consequently, it can produce shorter mean response times than no folding under medium to heavy loads;Also because of this efficiency improvement, dynamic policies that reduce waiting times by executing a large number of jobs simultaneously are more promising than schemes that limit the number of active jobs. However, limiting the number of active applications can be the superior approach when folding does not improve application efficiency

A (3/2+ɛ) approximation algorithm for scheduling malleable and non-malleable parallel tasks

In this paper we study a scheduling problem with malleable and non-malleable parallel tasks on $m$ processors. A non-malleable parallel task is one that runs in parallel on a specific given number of processors. The goal is to find a non-preemptive schedule on the $m$ processors which minimizes the makespan, or the latest task completion time. The previous best result is the list scheduling algorithm with an absolute approximation ratio of $2$. On the other hand, there does not exist an approximation algorithm for scheduling non-malleable parallel tasks with ratio smaller than $1.5$, unless $P=NP$. In this paper we show that a schedule with length $(1.5 +\epsilon) OPT$ can be computed for the scheduling problem in time $O(n \log n) + f(1/\epsilon)$. Furthermore we present an $(1.5 + \epsilon)$ approximation algorithm for scheduling malleable parallel tasks. Finally, we show how to extend our algorithms to the variant with additional release dates

Complex scheduling models and analyses for property-based real-time embedded systems

Modern multi core architectures and parallel applications pose a significant challenge to the worst-case centric real-time system verification and design efforts. The involved model and parameter uncertainty contest the fidelity of formal real-time analyses, which are mostly based on exact model assumptions. In this dissertation, various approaches that can accept parameter and model uncertainty are presented. In an attempt to improve predictability in worst-case centric analyses, the exploration of timing predictable protocols are examined for parallel task scheduling on multiprocessors and network-on-chip arbitration. A novel scheduling algorithm, called stationary rigid gang scheduling, for gang tasks on multiprocessors is proposed. In regard to fixed-priority wormhole-switched network-on-chips, a more restrictive family of transmission protocols called simultaneous progression switching protocols is proposed with predictability enhancing properties. Moreover, hierarchical scheduling for parallel DAG tasks under parameter uncertainty is studied to achieve temporal- and spatial isolation. Fault-tolerance as a supplementary reliability aspect of real-time systems is examined, in spite of dynamic external causes of fault. Using various job variants, which trade off increased execution time demand with increased error protection, a state-based policy selection strategy is proposed, which provably assures an acceptable quality-of-service (QoS). Lastly, the temporal misalignment of sensor data in sensor fusion applications in cyber-physical systems is examined. A modular analysis based on minimal properties to obtain an upper-bound for the maximal sensor data time-stamp difference is proposed

The work/exchange model: a generalized approach to dynamic load balancing

A crucial concern in software development is reducing program execution time. Parallel processing is often used to meet this goal. However, parallel processing efforts can lead to many pitfalls and problems. One such problem is to distribute the workload among processors in such a way that minimum execution time is obtained. The common approach is to use a load balancer to distribute equal or nearly equal quantities of workload on each processor. Unfortunately, this approach relies on a naive definition of load imbalance and often fails to achieve the desired goal. A more sophisticated definition should account for the affects of additional factors including communication delay costs, network contention, and architectural issues. Consideration of additional factors led us to the realization that optimal load distribution does not always result from equal load distribution. In this dissertation, we tackle the difficult problem of defining load imbalance. This is accomplished through the development of a parallel program model called the Generalized Work/Exchange Model. Associated with the model are equations for a restricted set of deterministically balanced programs that characterize idle time, elapsed time, and potential speedup. With the aid of the model, several common myths about load imbalance are exposed. A useful application called a load balancer enhancer is also presented which is applicable to the more general, quasi-static load unbalanced program

Design and analysis of load balancing/scheduling strategies on distributed computer networks using virtual routing approach

Ph.DDOCTOR OF PHILOSOPH

Multiprocessor System-on-Chips based Wireless Sensor Network Energy Optimization

Wireless Sensor Network (WSN) is an integrated part of the Internet-of-Things (IoT) used to monitor the physical or environmental conditions without human intervention. In WSN one of the major challenges is energy consumption reduction both at the sensor nodes and network levels. High energy consumption not only causes an increased carbon footprint but also limits the lifetime (LT) of the network. Network-on-Chip (NoC) based Multiprocessor System-on-Chips (MPSoCs) are becoming the de-facto computing platform for computationally extensive real-time applications in IoT due to their high performance and exceptional quality-of-service. In this thesis a task scheduling problem is investigated using MPSoCs architecture for tasks with precedence and deadline constraints in order to minimize the processing energy consumption while guaranteeing the timing constraints. Moreover, energy-aware nodes clustering is also performed to reduce the transmission energy consumption of the sensor nodes. Three distinct problems for energy optimization are investigated given as follows: First, a contention-aware energy-efficient static scheduling using NoC based heterogeneous MPSoC is performed for real-time tasks with an individual deadline and precedence constraints. An offline meta-heuristic based contention-aware energy-efficient task scheduling is developed that performs task ordering, mapping, and voltage assignment in an integrated manner. Compared to state-of-the-art scheduling our proposed algorithm significantly improves the energy-efficiency. Second, an energy-aware scheduling is investigated for a set of tasks with precedence constraints deploying Voltage Frequency Island (VFI) based heterogeneous NoC-MPSoCs. A novel population based algorithm called ARSH-FATI is developed that can dynamically switch between explorative and exploitative search modes at run-time. ARSH-FATI performance is superior to the existing task schedulers developed for homogeneous VFI-NoC-MPSoCs. Third, the transmission energy consumption of the sensor nodes in WSN is reduced by developing ARSH-FATI based Cluster Head Selection (ARSH-FATI-CHS) algorithm integrated with a heuristic called Novel Ranked Based Clustering (NRC). In cluster formation parameters such as residual energy, distance parameters, and workload on CHs are considered to improve LT of the network. The results prove that ARSH-FATI-CHS outperforms other state-of-the-art clustering algorithms in terms of LT.University of Derby, Derby, U