Optimal scheduling for two-processor systems

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.)

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.

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.

Contention-aware optimal scheduling of real-time precedence-constrained task graphs on heterogeneous distributed systems

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.

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.

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.

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.

Changes in our electricity supply chain are causing a paradigm shift from centralized control towards decentralized energy management. Within the framework of decentralized energy management, devices that offer flexibility in their load profile play an important role. These devices schedule their flexible load profile based on steering signals received from centralized controllers. The problem of finding optimal device schedules based on the received steering signals falls into the framework of resource allocation problems. We study an extension of the traditional problems studied within resource allocation and prove that a divide-and-conquer strategy gives an optimal solution for the considered extension. This leads to an efficient recursive algorithm, with quadratic complexity in the practically relevant case of quadratic objective functions. Furthermore, we study discrete variants of two problems common in decentralized energy management. We show that these problems are NP-hard and formulate natural relaxations of both considered discrete problems that we solve efficiently. Finally, we show that the solutions to the natural relaxations closely resemble solutions to the original, hard problems.

Minimizing makespan subject to minimum total flow-time on identical parallel machines

This paper proposes an optimal day-ahead optimization schedule for gas-electric integrated energy system (IES) considering the bi-directional energy flow. The hourly topology of electric power system (EPS), natural gas system (NGS), energy hubs (EH) integrated power to gas (P2G) unit, are modeled to minimize the day-ahead operation cost of IES. Then, a second-order cone programming (SOCP) method is utilized to solve the optimization problem, which is actually a mixed integer nonconvex and nonlinear programming issue. Besides, cutting planes are added to ensure the exactness of the global optimal solution. Finally, simulation results demonstrate that the proposed optimization schedule can provide a safe, effective and economical day-ahead scheduling scheme for gas-electric IES.

Computation and communication schedule optimization for data-sharing tasks on uniprocessor

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

Freshness of information is of critical importance for a host of applications of wireless communications. In order to deliver information from multiple sources in a timely and fair fashion through a wireless channel, we propose optimizing the link scheduling strategy in respect of age of information, which is a newly introduced metric that measures how fresh information is. Specifically, we consider a set of co-channel links, each having a number of packets to be delivered, and address the problem that aims to find the optimal scheduling solution, such that the maximum peak age of information is minimized. We mathematically formulate this so-called min-max peak age scheduling problem (MPASP), and prove it is NP-hard. Theoretical insights including tractable cases and optimality properties are derived. For problem solution, an integer linear programming (ILP) formulation is proposed. We also develop a sub-optimal, but fast, algorithm to solve the problem with better scalability. Numerical study shows that, by employing the optimal schedule, the maximum peak age is significantly reduced in comparison to other classic scheduling strategies such as minimum-time scheduling.

Two-stage heuristic procedure for scheduling job shops