Showing papers on "Fair-share scheduling published in 1978"
TL;DR: This work studies the problem of scheduling periodic-time-critical tasks on multiprocessor computing systems and considers two heuristic algorithms that are easy to implement and yield a number of processors that is reasonably close to the minimum number.
Abstract: We study the problem of scheduling periodic-time-critical tasks on multiprocessor computing systems. A periodic-time-critical task consists of an infinite number of requests, each of which has a prescribed deadline. The scheduling problem is to specify an order in which the requests of a set of tasks are to be executed and the processor to be used, with the goal of meeting all the deadlines with a minimum number of processors. Since the problem of determining the minimum number of processors is difficult, we consider two heuristic algorithms. These are easy to implement and yield a number of processors that is reasonably close to the minimum number. We also analyze the worst-case behavior of these heuristics.
616 citations
TL;DR: An O(n) t~me algorithm is presented to obtain an opt,mal fimsh time preemptive schedule for n independent tasks on m uniform processors.
Abstract: AaSTRACT An O(n) t~me algorithm is presented to obtain an opt,mal fimsh time preemptive schedule for n independent tasks on m uniform processors This algorithm assumes that the tasks are lnmally ordered by task length and that the umform processors are ordered by processor speed
218 citations
TL;DR: In this article, the authors examined and extended previous analytical work on the scheduling of stacker cranes in automatic warehousing systems by means of a computer simulation, and demonstrated the value of previously-proposed scheduling rules in a dynamic, stochastic environment operating with imperfect information.
Abstract: This paper examines and extends previous analytical work on the scheduling of stacker cranes in automatic warehousing systems. In particular, the following are examined by means of a computer simulation: (1) The performance of the closest-open-location rule compared to random storage assignment; (2) The dynamic behavior of the system under stochastic conditions, using various crane and rack utilization levels; (3) The actual versus predicted reduction in crane travel time due to improved scheduling rules; (4) The effect of imperfect information concerning the length of stay of an incoming pallet on system performance. The results of our experiments provide evidence in support of the proposed analytical models. Most important, the experiments demonstrate the value of previously-proposed scheduling rules in a dynamic, stochastic environment operating with imperfect information.
160 citations
TL;DR: This paper presents an introduction to this approach to scheduling by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible.
Abstract: One approach to coping with the apparent difficulty of many schedule-optimization problems, such as occur in machine shops and computer processing, is to devise efficient algorithms that find schedules guaranteed to be "near-optimal." This paper presents an introduction to this approach by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible. The paper concludes with a brief survey of what has been accomplished to date in the area of scheduling using this approach.
149 citations
TL;DR: For this problem, it is shown that there is a 0n2-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that ri.
Abstract: We consider a class of n-job one-machine scheduling problems with ready time ri, processing time pi, and due time di for each job i. Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0n2-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that ri
145 citations
136 citations
16 Oct 1978
TL;DR: The problem is to find a feasible schedule in which each job is run for the same amount of time p, and the processing is nonpreemptive in that once a job is started it continues executing until it has run for precisely p units of time.
Abstract: Suppose we are given a single processor and a set S of n jobs. For each job X there is a release time rx and a deadline dx , with rx and dx nonnegative real numbers. A schedule is feasible if there is no time at which more than one job is being run and if every job in the schedule is begun no earlier than its release time and is completed by its deadline. The problem is to find a feasible schedule in which each job is run for the same amount of time p. The processing is nonpreemptive in that once a job is started it continues executing until it has run for precisely p units of time.
96 citations
TL;DR: A more efficient algorithm than the existing one is presented for a single-machine scheduling problem where penalties occur for jobs that either commence before their target start date or are completed after their due date.
Abstract: We consider a single-machine scheduling problem where penalties occur for jobs that either commence before their target start date or are completed after their due date. The objective is to minimize the maximum penalty subject to certain assumptions on the target start times, due dates, and penalty functions. A more efficient algorithm than the existing one is presented for this problem. The number of computations in the proposed algorithm is of the order of n log n, while in the existing algorithm it is of the order of n2.
57 citations
TL;DR: In this article, the scheduling of multiple products with stochastic demand on a single machine system was modelled and simulation of six scheduling rules under varying cost and system parameters was performed.
Abstract: The scheduling of multiple products with stochastic demand on a single machine system was modelled. Simulation of six scheduling rules under varying cost and system parameters was performed. It was shown that several of the commonly proposed rules resulted in very costly schedules. It was also shown that the best scheduling rule for a particular system depends on the number of products, distribution of demand among those products, and the proportion of capacity utilization, as well as on the relative costs for carrying inventory, setup, and shortages.
54 citations
TL;DR: This paper reports on two heuristic procedures, one which uses the two-phase approach, and one which deals directly with the employee scheduling problem.
35 citations
TL;DR: In this paper, the problem of group scheduling on a single stage to minimize total tardiness is considered, where jobs are classified into several groups on the basis of group technology and the optimal decision as to scheduling sequences will be made as to product group and specific job.
Abstract: This paper considers the problem of group scheduling on a single stage to minimize total tardiness. It is assumed that jobs are classified into several groups on the basis of group technology. Optimal decision as to scheduling sequences will be made as to product group and specific job. This paper proves basic theorems that establish the relative order in which pairs of groups are processed in an optimal schedule. In general, scheduling problems of moderate size may be at least partially ordered so that very few schedules remain to be searched. Two practical algorithms for determining the optimal group schedule and the near optimal group schedule are proposed. Numerical examples are presented in detail.
TL;DR: This investigation shows that much is to be expected from the dual approach for more complex scheduling problems while dynamic programming deserves a new research effort because of its efficiency in special structured problems and/or problems where a posteriori precedence relations (dominance criteria) can be developed.
TL;DR: A goal programming model for coordinating the production of an aggregate schedule which is to be fed into the detailed scheduling package currently employed is developed and discussed.
Abstract: The paper introduces mi overall scheduling problem. One crucial aspect is identified; this is the production of an aggregate schedule which is to be fed into the detailed scheduling package currently employed. The problem is seen to be that of achieving a balance between a smooth work-load on the factory floor and matching production with promised delivery dates. A goal programming model for this coordination is developed and discussed. Numerical examples illustrating the approach are presented, and computational experience is discussed.
TL;DR: This work introduces a combinatorial approach for studying multiple-processor scheduling problems that involve the preemptive scheduling of independent jobs and seeks dynamic algorithms that make scheduling decisions based on changing information.
Abstract: We introduce a combinatorial approach for studying multiple-processor scheduling problems that involve the preemptive scheduling of independent jobs. Unlike most combinatorial models used for studying scheduling problems, ours assumes that jobs arrive over time but that scheduling decisions must be made without knowledge of what jobs will arrive in the future. We seek dynamic algorithms that make scheduling decisions based on changing information. An algorithm is considered to be "optimal" only if it consistently produces schedules no worse than those produced by any omniscient algorithm that has exact knowledge of attributes of all jobs in advance. Measures of performance examined include the maxima and means of completion time, flow time, and lateness. "Optimal" algorithms are established in a few cases, while it is determined in other cases that such "optimal" algorithms require more information than the model provides.
10 Oct 1978
TL;DR: Theorems are proved concerning the feasibility of the second stage algorithm, and the upper bound on the number of preemptions in the optimal schedule is proved.
Abstract: The problem considered is that of scheduling n preemptable tasks on m parallel processors, when each task requires for its processing a processor and one resource unit from the set of additional resources. The processing times of a task on different processors are unrelated. We present the method for solving this problem which is composed of two stages. In the first stage, a linear programming problem is solved giving the minimum schedule length and optimal task processing times on particular processors. On the basis of this solution, in the second stage the optimal schedule is constructed taking into account the resource constraints. Theorems are proved concerning the feasibility of the second stage algorithm, and the upper bound on the number of preemptions in the optimal schedule. The cases of independent and dependent tasks are considered.
TL;DR: The heuristic algorithm was found to yield better average performance than the integer programming solution, although the differences were not statistically significant.
Abstract: This paper presents an analysis and comparison of scheduling algorithms for the unbalanced production line. A new heuristic algorithm is presented accompanied by an index for classifying the configuration of a production line. A factorial experiment was conducted in order to determine those factors which were significant with respect to the performance measure under consideration, the average cost of holding in-process inventory. Additional analyses were then performed on the line factors and scheduling algorithms with appropriate conclusions drawn. The best performing algorithm was then compared to the performance of Single Period integer programming over a multiple time frame. The heuristic algorithm was found to yield better average performance than the integer programming solution, although the differences were not statistically significant. Recommendations concerning the implementation of the heuristic algorithm are provided.
TL;DR: In this article, a new approach based on a hierarchical decomposition of the production control system and of the decision-making techniques is proposed for plants working in small and medium size lots only.
Abstract: The purpose of this communication is to introduce a new approach in the field of production-control with regard to plants working in small and medium size lots only. In order to suppress the disadvantages of the systems already in use, the GRAI proposes a now approach which is based on a hierarchical decomposition of the production control system and of the decision-making techniques. There will be first a description of the new structure, then u description of two applications corresponding to two elements of the structure, namely: (a) a conversational system for a quick calculation of the long-range production plans; (b) the aided dynamic scheduling.
TL;DR: An algorithm is presented that is easy to program, requires little computation and, under certain restrictive assumptions, provides an optimal solution to the mission scheduling problem of the NASA space-shuttle program.
Abstract: The mission scheduling problem of the NASA space-shuttle program requires a selection of mission launch times that minimize the number of missions flown late and that satisfy early start time and resource constraints. We present an algorithm for this problem that is easy to program, requires little computation and, under certain restrictive assumptions, provides an optimal solution. Computational experience with a test case is discussed.
TL;DR: A class of production scheduling problems which can be modeled as network flow problems which are addressed under the assumption that production occurs in batches is considered.
Abstract: This paper considers a class of production scheduling problems which can be modeled as network flow problems. The problems are addressed under the assumption that production occurs in batches. We also require that the cost function be convex and separable. The model applies for a number of well known production scheduling problems and will handle multiple products and multiple facilities.
TL;DR: Model studies of some integrated, feedback-driven scheduling systems for multiprogrammed-multiprocessor computer systems are presented and even relatively simple dynamic schedulers are shown to improve system performance over that given by optimal or near-optimal static Schedulers imbedded in identical system structures and workload environments.
Abstract: Model studies of some integrated, feedback-driven scheduling systems for multiprogrammed-multiprocessor computer systems are presented The basic control variables used are the data-flow rates for the processes executing on the CPU The model systems feature simulated continuous-flow and preempt-resume scheduling of input-output activity Attention is given to the amount of memory resource required for effective processing of the I/O activity (buffer space assignment) The model studies used both distribution-driven and trace-driven techniques Even relatively simple dynamic schedulers are shown to improve system performance (as measured by user CPU time) over that given by optimal or near-optimal static schedulers imbedded in identical system structures and workload environments The improvement is greatest under a heavy I/O demand workload
TL;DR: It can be shown that due to the special structure of the derived mathematical model, an optimal schedule may be found by a few arithmetic steps without the computer assistance which other existing methods require.
Abstract: This paper presents a simple solution algorithm to the problem of scheduling workforce for an organization operated seven days a week. For a given number of full-time workers, the objective is to maximize the total number of workers who get two consecutive days off. It can be shown that due to the special structure of the derived mathematical model, an optimal schedule may be found by a few arithmetic steps without the computer assistance which other existing methods require.
TL;DR: It is shown that the combinatorial problem of scheduling jobs of equal duration with tardiness costs and resource limitations can be solved by formulating the problem as a classical transportation model which is here highly degenerate.
Abstract: In this paper it is shown that the combinatorial problem of scheduling jobs of equal duration with tardiness costs and resource limitations can be solved by formulating the problem as a classical transportation model which is here highly degenerate. A new algorithm derived from the classical stepping stone method is given. The algorithm produces a strict decrease of the objective at each iteration. A special case which could be called the simplest problem of scheduling is also studied.
TL;DR: A special-purpose task scheduler is described which is suitable for many dedicated, real-time minicomputer and microcomputer applications and its memory size is estimated at about 1 kbyte, using the Intel 8080 instruction set.
Abstract: A special-purpose task scheduler is described which is suitable for many dedicated, real-time minicomputer and microcomputer applications. The scheduling algorithm is presented in detail. A brief discussion of a basic interrupt-driven real-time executive (RTE) is also included. Its memory size is estimated at about 1 kbyte, using the Intel 8080 instruction set.
TL;DR: This paper addresses the problem of maximizing the number of jobs completed in an environment where each job is in competition with other jobs for certain scarce resources.
Abstract: The scheduling of tasks (such as jobs through a com puter, different pulses through a radar system, or machining efforts through a production line) is a problem that is encountered quite frequently in practice. Traditionally, analysts have endeavored to develop schedules that minimize make-span (the time that elapses between the start of the first task in a sequence until the finish of the last task in a sequence). However, there are often many other appropriate measures of scheduling effectiveness. In this paper we address the problem of maximizing the number of jobs completed in an environment where each job is in competition with other jobs for certain scarce resources. Further, we shall assume that the number of jobs and possible start times is so large as to eliminate the possibility of the use of any exact technqiue.
TL;DR: A system embodying an approach to job scheduling that permits a large family of scheduling strategies to be implemented via different priority calculation schemes is discussed as an application of the approach to other types of systems.
Abstract: The job-scheduling function in a multiprogramming computer system plays a key role in the achievement of the performance goals for the system. It is possible and convenient to partition this scheduling function into a priority assignment function and resource assignment function. Implementation of a general purpose resource assignment module permits a large family of scheduling strategies to be implemented via different priority calculation schemes. The implications of this partitioning of the scheduling function are studied by use of a simulation model. A system embodying this approach to job scheduling is discussed as an application of the approach to other types of systems.
TL;DR: A new approach to the scheduling of work, now in service on the IBM 370/165 at Cambridge University, England, which represents a fundamental change in scheduling philosophy from the usual ‘first in first out’ or ‘priority with ageing’ approach, to a ‘now or later’ system.
Abstract: This paper is a sequel to ‘Scheduling for a share of the machine’,1 and describes a new approach to the scheduling of work, now in service on the IBM 370/165 at Cambridge University, England. The new approach provides large amounts of immediate turnround while retaining the essential features of the older system, predictability, control of machine usage proportional to shares and ‘fairness’. The approach in this paper, whilst being a natural extension of the Share system, represents a fundamental change in scheduling philosophy from the usual ‘first in first out’ or ‘priority with ageing’ approach, to a ‘now or later’ system. It is believed to be original, and to represent an important development in optimizing waiting time, be it for computer time or for hospital beds.
TL;DR: An experiment found Holt's scheduling rules may not be effective if costs are non-quadratic, which may explain the relative lack of use of these rules in industry.
Abstract: Holt at al. (1960) modollod the production scheduling problem with quadratic costs and derived an optimal set of scheduling rules. Our experiment found those rules may not be effective if costs are non-quadratic. This may explain the relative lack of use of these rules in industry.
01 Jan 1978
TL;DR: The results from this analysis indicates that this dynamic priority scheduling rule can be applied favorably to transaction processing systems.
Abstract: : This report describes the investigation of a dynamic priority scheduling rule and its applicability for scheduling transaction processing systems. In this report once the scheduling rule was chosen, various cost models were optimized using this rule. Simulation studies were also conducted using this rule. The results from this analysis indicates that this scheduling rule can be applied favorably to transaction processing systems. (Author)