An optimal scheduling algorithm for minimizing the computing period of cyclic synchronous tasks on multiprocessors

We present a jointly optimal selection and scheduling scheme for the lossy transmission of frames governed by a dependency relation and a delay constraint over a link with limited capacity. A main application for this is scalable video streaming. Our objective is to select a subset of frames and decide their transmission schedule such that the overall video quality at the receiver is maximized. The problem is solved for two of the most common classes of dependency structures for video encoding, which include as a special case the popular hierarchical dyadic structure. We formally characterize the structural properties of an optimal transmission schedule in terms of frame dependency. It is shown that regardless of the subset of frames selected for transmission, any optimal schedule has an equivalent canonical form that is a subsequence of a unique universal sequence containing all frames. The canonical form can be computed efficiently through the construction of a dependency tree. This leads to separable but jointly optimal frame selection and scheduling algorithms that have quadratic computational complexity in the number of frames. Simulation with video traces demonstrates that the optimal scheme can substantially outperform existing suboptimal alternatives.

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

Approximate optimal periodic scheduling of multiple sensors with constraints

We analyze a human and multi-robot collaboration system and propose a method to optimally schedule the human attention when a human operator receives collaboration requests from multiple robots at the same time. We formulate the human attention scheduling problem as a binary optimization problem which aims to maximize the overall performance among all the robots, under the constraint that a human has limited attention capacity. We first present the optimal schedule for the human to determine when to collaborate with a robot if there is no contention occurring among robots' collaboration requests. For the moments when contentions occur, we present a contention-resolving Model Predictive Control (MPC) method to dynamically schedule the human attention and determine which robot the human should collaborate with first. The optimal schedule can then be determined using a sampling based approach. The effectiveness of the proposed method is validated through simulation that shows improvements.

We consider a reader-writer system consisting of a single server and a fixed number of jobs (or customers) belonging to two classes. Class one jobs are called readers and any number of them can be processed simultaneously. Class two jobs are called writers and they have to be processed one at a time. When a writer is being processed no other writer or readers can be processed. A fixed number of readers and writers are ready for processing at time 0. Their processing times are independent random variables. Each reader and writer has a fixed waiting cost rate. We find optimal scheduling rules that minimize the expected total waiting cost (expected total weighted flowtime). We consider both nonpreemptive and preemptive scheduling. The optimal nonpreemptive schedule is derived by a variation of the usual interchange argument, while the optimal schedule in the preemptive case is given by a Gittins index policy. These index policies continue to be optimal for systems in which new writers enter the system in a Poisson fashion.

In the Digital Age, many new tools have emerged through the use of advanced monitoring systems and relatively low cost, powerful computation. In particular, system Reliability increases have been achieved through various applications of remote monitoring. Mathematical optimization applied to scheduling has been used in many industries to lower costs successfully, generally as a planning tool. More recently, it has found application in day-to-day operational planning for the heavy industries of power generation and oil and gas, since computation time has decreased down to minutes instead of days. Combining this with the powerful improvements in statistical and machine learning forecasting, the intersection of these domains has resulted in operational optimization. Combining maintenance planning models into the operational optimization framework provides operators with the opportunity to extend maintenance intervals purely based on optimized scheduling, which costs nearly nothing compared with having to purchase new parts to achieve extended time between maintenance. When the application involves drivers utilizing carbon based fuels, it is often true that the optimized schedule results in reduced emissions compared with typical base-case operation, which in many locations can result in further cost reductions. In this paper we propose a framework for scheduling machines at a particular location such that no machine exceeds a certain threshold, t¯, in running time. In particular, the solution attempts to push the facility-wide time between maintenance sessions to some operator defined limit higher than any individual unit’s required time between maintenance. The framework utilizes Mixed Integer Programming with partially stochastic demand forecasts to solve for optimal running schedules through Monte Carlo simulation. Optimality of a running schedule is based on multiple factors including ability to meet the demand forecast, number of starts required, start-reliability and possible over-fire of engines. The resulting set of solutions provide a likelihood of success in reaching a given site level extended time between maintenance. Operators can use this framework to determine how far the time between maintenance can be extended and determine the probability that a given extension can actually be realized at the physical site. This framework can also be used at managerial levels that consider personnel planning and future capital expenditures.

The use of multiple digital signal processors (DSPs) to implement a real-time digital controller is described. Specially, the multi-DSP implementation of a multi-input single-output digital controller with small sampling period and throughput time is considered. The optimal scheduling problem to achieve the minimum sampling period when the number of available DSPs is fixed is formulated. A scheduling algorithm based on a branch-and-bound approach for the optimization problem is then proposed. The multi-DSP system has also been realized experimentally. The proposed algorithm has been implemented and tested by a breadboard experiment using three DSPs. >

Two-stage heuristic procedure for scheduling job shops

It is a great challenge to find an optimal one-wafer cyclic schedule for a single-arm multicluster tool that is widely adopted in semiconductor fabrication. Aiming to tackle this significant problem, an optimal scheduling strategy is determined first for each individual tool under the condition that the bottleneck individual tool is transport-bound. Then, by developing a Petri net model with robot waiting being explicitly described to reveal the properties of the entire system, this paper shows that to schedule such a tool optimally is to allocate the robot waiting time properly. Then, this paper presents the necessary and sufficient conditions for the existence of an optimal one-wafer cyclic schedule. Thereafter, an efficient algorithm is developed to check the given conditions and find such a schedule efficiently if existing. Finally, two industrial examples are used to verify that the proposed method is applicable and effective.

A set of tasks {T1, T2, ..., Tr] are to be scheduled on a two-processor computing system. The execution time of each of the tasks is given. Moreover, a partial ordering ≪ over the set of tasks is specified. If Ti ≪ Tj, it is required that the execution of Tj will not begin until the completion of the execution of Ti. Let ω denote the total elapsed time for the execution of all the tasks in the set when an optimal non-preemptive schedule is used. Let ω′ denote the total elapsed time for the execution of all the tasks in the set when an optimal preemptive schedule is used. Trivially, we know that ω ≥ ω′ However, it can be shown that ω′ ≥ 3/4 ω This result can be extended to an n-processor computing system. In this case, ω′ ≥ n+1/2n ω Moreover, these are best possible bounds. A possible interpretation of the results is: The installation of a high speed drum in a two-processor computing system will increase the operation speed of the system by at most 25%. For an n-processor system, the increment is at most 50%. (The installation of a high speed drum enables us to interrupt the execution of tasks at will.)

Task Scheduling is one of the key elements in any distributed-memory machine (DMM), and an efficient algorithm can help reduce the interprocessor communication time. As optimal scheduling of tasks to DMMs is a strong NP-hard problem, many heuristic algorithms have been introduced in the literature. This paper presents a Task Duplication based Scheduling (TDS) algorithm which can schedule directed acyclic graphs (DAGs) with a complexity of O(|V|/sup 2/), where |V| is the number of tasks in the DAG. This algorithm generates an optimal schedule for a class of DAGs which satisfy a simple cost relationship. The performance of the algorithm has been observed by its application to some practical DAGs, and by comparing it with other existing scheduling schemes in terms of the schedule length and algorithm complexity.

The maximum matching algorithm for bipartite graphs can be used to provide optimal scheduling for crossbar based interconnection networks. Unfortunately, maximum matching requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) time for an N times N communication system, which has limited its application to real-time network scheduling. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By taking advantage of the inherent parallelism available in custom hardware design, we introduce three maximum matching implementations in hardware and show how we can trade design complexity for performance. Specifically, we examine a pure logic scheduler with three dimensions of parallelism, a matrix scheduler with two dimensions of parallelism and a vector scheduler with one dimension of parallelism. These designs reduce the algorithmic time complexity down to O(1), O(K), and O(KN), respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K=2N-1 steps, our simulation results show that the scheduler can achieve 99% of the optimal schedule when K=9. We examine hardware and time complexity of these architectures for crossbar sizes of up to N=1024. Using FPGA synthesis results, we show that a greedy schedule for various sized crossbars, ranging from 8 times 8 to 256 times 256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024 times 1024 the scheduling can be completed in approximately 10 s with current technology and could reach under 90 ns with future technologies

The maximum matching algorithm for bipartite graphs can be used to provide optimal scheduling for crossbar based interconnection networks. Unfortunately, maximum matching requires O(N3) time for an N x N communication system, which has limited its application to real-time network scheduling. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By taking advantage of the inherent parallelism available in custom hardware design, we introduce three Maximum Matching implementations in hardware and show how we can trade design complexity for performance. Specifically, we examine a Pure Logic Scheduler with three dimensions of parallelism, a Matrix Scheduler with two dimensions of parallelism and a Vector Scheduler with one dimension of parallelism. These designs reduce the algorithmic time complexity down to O(1), O(K), and O(KN), respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K = 2N -- 1 steps, our simulation results show that the scheduler can achieve 99% of the optimal schedule when K = 9. We examine hardware and time complexity of these architectures for crossbar sizes of up to N = 1024. Using FPGA synthesis results, we show that a greedy schedule for various sized crossbars, ranging from 8 x 8 to 256 x 256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024 x 1024 the scheduling can be completed in approximately 10 μs with current technology and could reach under 90 ns with future technologies.

With increased uncertainties and depressed security margins of distribution networks, the risk of violating load or voltage constraints has increased. The usual risk-prevention method is to set an appropriate optimal schedule of active distribution networks to reserve enough margin without incurring extra operating costs. In this study, an optimal scheduling method for an active distribution network is proposed that allows for a low level of violation risk to minimize operating costs while maintaining good system security. Overload violation risk cost is a financial cost due to the cost of countermeasures needed to avoid overload violation. In this study, the N-0 security regions of overload are set as the constraint that provides the definition and calculation of the bidirectional violation distance of overloading for active distribution networks based on the N-0 security region. The relationship between the violation distance of overloading and the countermeasures against overload violation have been established based on the power flow equations, enabling the calculation of the countermeasures cost. The assessment model for the overload violation risk cost is derived from the cost of countermeasures and probability distributions of nodal power. The point estimation algorithm is introduced to simplify the calculation. The calculation of risk cost is fixed through the conditional value-at-risk. On this basis, a novel optimization scheduling model of active distribution networks that considers risk cost is constructed. Examples of the optimal schedule are designed and the validity of the proposed method is verified.

Mixed integer linear programming (MILP) has been gaining traction as a method for solving optimal pump scheduling problems in water distribution networks (WDNs). However, inclusion of variable speed pumps (VSPs) in MILP pump scheduling frameworks has not been given adequate treatment. This article addresses this gap by describing a methodology for formulating and solving optimal pump scheduling problems with VSPs using MILP and piece-linear approximations of network components. The methodology proceeds in four steps: (a) WDN simulation with initial pump schedule(s), (b) approximation of network components, including VSP, using linear and piece-linear functions around the chosen operating points, (c) formulation of a fully parameterised mixed integer linear programme, and (d) solution of the optimisation problem and WDN simulation with optimal pump schedule(s). The methodology is coded in MATLAB/OCTAVE and Python and is publicly available on GitHub. It was applied to solve a pump scheduling problem on a two variable speed pump single-tank network that allows the reader to easily understand how the methodology works and how it is applied in practice. The results show that the formulation is robust and the optimiser is able to return a globally optimal solution for a range of operating points.