Showing papers on "Scheduling (computing) published in 1978"
TL;DR: This work considers one of the basic, well-studied problems of scheduling theory, that of nonpreemptively scheduling n independent tasks on m identical, parallel processors with the objective of minimizing the number of overlapping tasks.
Abstract: We consider one of the basic, well-studied problems of scheduling theory, that of nonpreemptively scheduling n independent tasks on m identical, parallel processors with the objective of minimizing...
667 citations
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: The use of precedence constraints between jobs that have to be respected in every feasible schedule is illustrated by extending some typical NP-completeness results and simplifying their correctness proofs for scheduling problems involving precedence constraints.
Abstract: Precedence constraints between jobs that have to be respected in every feasible schedule generally increase the computational complexity of a scheduling problem. Occasionally, their introduction may turn a problem that is solvable within polynomial time into an NP-complete one, for which a good algorithm is highly unlikely to exist. We illustrate the use of these concepts by extending some typical NP-completeness results and simplifying their correctness proofs for scheduling problems involving precedence constraints.
589 citations
01 Oct 1978
587 citations
TL;DR: An integer programming algorithm for allocating limited resources to competing activities jobs, tasks, etc. of a project such that the completion time of the project is minimal among all possible completion times is described.
Abstract: In this paper we describe an integer programming algorithm for allocating limited resources to competing activities jobs, tasks, etc. of a project such that the completion time of the project is minimal among all possible completion times. Typical of such problems is the minimization of the completion time of projects of the PERT/CPM variety where limits on resource availability force the postponement of selected activities during project performance. Also included in this class of problems for which our procedure is applicable is the assignment of jobs to machines such that the elapsed time for completing all jobs makespan is a minimum over all possible job-machine assignments.
The procedure developed consists of a systematic evaluation enumeration of all possible job finish times for each task in the project. To limit the number of task assignments which have to be explicitly evaluated, an artifice called a network cut is developed which removes from consideration the evaluation of job finish times which cannot lead to a reduced project completion time. Results reported demonstrate that the procedure developed is a reliable optimization technique for projects consisting of up to 30--50 jobs and three different resource types. The procedure is particularly applicable in those instances in which computer primary storage is limited. Many of the mini-computers available today are capable of implementing our approach without extensive programming being required for writing to auxiliary storage, making the technique available to the project manager in those environments in which extensive computer resources for scheduling are not readily available.
225 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
IBM1
TL;DR: An analytic investigation into the fundamental aspects of scheduling “Dial-a-Ride” transportation systems is conducted and a class of algorithms is derived for which performance can be measured in a precise asymptotic probabilistic sense.
Abstract: An analytic investigation into the fundamental aspects of scheduling “Dial-a-Ride” transportation systems is conducted. Based upon simple mathematical models that focus on the combinatorial nature of the problem, a class of algorithms is derived for which performance can be measured in a precise asymptotic probabilistic sense. The approach yields many qualitative insights and the resulting transportation schemes have many attractive practical features. For example, they have modest computational requirements, are decentralized, and are easy to visualize and implement.
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: The basic structure of this vehicle routing and scheduling problem, formulate the street-sweeper routing problem, and explain the algorithm are presented and the computer implementation based on this algorithm is described.
Abstract: This paper discusses a computer-assisted method for routing and scheduling street sweepers in a municipality. We present the basic structure of this vehicle routing and scheduling problem, formulate the street-sweeper routing problem, and explain the algorithm. The computer implementation based on this algorithm is then described. Computational experience with the system in New York City and Washington, D.C., is presented and the obstacles to and successes with implementation are discussed.
97 citations
TL;DR: It is shown that improved solutions can be obtained by having a visual, dynamic representation of a job-shop problem, and visual interactive simulation methods can be used for this purpose.
Abstract: This paper describes the use of the job-shop scheduling problem in order to investigate the potential of visual interactive simulation methods. Batch simulation methods are compared with visual interactive simulation methods for the job-shop problem. The paper shows that improved solutions can be obtained by having a visual, dynamic representation of a job-shop problem.
53 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.
TL;DR: Results and computational experience that were obtained from implementing the model in a large bus company are presented and an efficient algorithm is developed.
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: The MERT operating system supports multiple operating system environments and permits processes to control scheduling parameters, which allow applications to be implemented as several independent, cooperating processes.
Abstract: The MERT operating system supports multiple operating system environments. Messages provide the major means of inter-process communication. Shared memory is used where tighter coupling between processes is desired. The file system was designed with real-time response being a major concern. The system has been implemented on the DEC PDP-11/45 and PDP-11/70 computers and supports the UNIX∗ time-sharing system, as well as some real-time processes. The system is structured in four layers. The lowest layer, the kernel, provides basic services such as inter-process communication, process dispatching, and trap and interrupt handling. The second layer comprises privileged processes, such as I/O device handlers, the file manager, memory manager, and system scheduler. At the third layer are the supervisor processes which provide the programming environments for application programs of the fourth layer. To provide an environment favorable to applications with real-time response requirements, the MERT system permits processes to control scheduling parameters. These include scheduling priority and memory residency. A rich set of inter-process communication mechanisms including messages, events (software interrupts), shared memory, inter-process traps, process ports, and files, allow applications to be implemented as several independent, cooperating processes. Some uses of the MERT operating system are discussed.
TL;DR: Numerical results indicate that the GSMA scheme offers substantially higher channel utilization compared to the synchronous time-division multiple access (STDMA) scheme, particularly at the low throughput region.
Abstract: A global scheduling multiple access (GSMA) scheme for data communication via a high speed bus is described. The GSMA scheme, which has a variable length frame format and the desirable property of guaranteeing each active user a minimum service per frame, attains conflict-free multiaccess and has the flexibility of providing more channel capacity to the large users. An expression for the mean system delay under a Poisson arrival law and an imbalanced loading (multi-rate) environment is derived. Numerical results indicate that the GSMA scheme offers substantially higher channel utilization compared to the synchronous time-division multiple access (STDMA) scheme, particularly at the low throughput region. It is shown also that the GSMA system offers superior delaythroughput performance to an STDMA or POLLING system.
TL;DR: A goal programming model is developed and demonstrated via a case example of the multi-product scheduling problem when multiple objectives exist and the various solution approaches to the problem are presented.
17 Jul 1978
TL;DR: In this paper, the authors defined the concurrent programming control problem of mutual exclusion in the framework of data spaces and introduced the size of the shared message variable as a machine-independent complexity measure for the effort of implementing scheduling schemes for mutual exclusion.
Abstract: The concurrent programming control problem of mutual exclusion can be precisely defined in the framework of data spaces The size of the shared message variable is introduced as a machine-independent complexity measure for the effort of implementing scheduling schemes for mutual exclusion Along the lines of a minimal solution for two-processor mutual exclusion using a three-valued message variable, a general n-processor solution is developed using uninterruptable test-and-set instructions on a (2n-1)-valued message variable
TL;DR: This paper analyzes the queueing and scheduling delays of the multiaccess model for satellite packet switching using an M/D/N queue and emplys a round-robin scheduling assignment algorithm, and results indicate that random transmission improves the queues performance.
Abstract: The multiaccess model for satellite packet switching proposed by the authors [1] employs a frame format, with scheduling assignments broadcast from the satellite. The total delay recurred by a data packet in traversing the satellite channel consists of queueing delay, scheduling delay, transmission delay and propagation delay. In this paper we analyze the queueing and scheduling delays and compare the analytical and simulation results. For the queuemg delay analysis we model the multiaccess scheme using an M/D/N queue, where N is the number of slots per frame. For the scheduling delay analysis we emply a round-robin scheduling assignment algorithm. We treat the cases with and without random transmission; our results indicate that random transmission improves the queueing delay performance.
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: Three graphic methods of presenting scheduling information were compared with each other and with a conventional, numerical presentation, and all three proved more effective than the numerical presentation in helping the subjects produce efficient schedules.
Abstract: Three graphic methods of presenting scheduling information were compared with each other and with a conventional, numerical presentation. The graphic methods were based on the Gantt chart, and all three proved more effective than the numerical presentation in helping the subjects produce efficient schedules. One method in particular which used a machines-by-time organization and identified machines by color code proved superior to the others. This is explained in terms of the perceptual nature of problem solution using these methods. It is suggested that this organization of information be adopted when the primary criterion for schedule evaluation is machine utilization and there are limitations on the display space and color-coding available.
03 Apr 1978
TL;DR: This paper proposes a pipeline model in which priority buffers are provided at every segment to control the flow of tasks, and shows that the theoretical maximum throughput of a pipeline is attainable with the use of internal buffers.
Abstract: Concurrent or overlapped processing of more than one task is a common technique used in many computer architectures to increase the throughput. A pipeline is one such form consisting of a set of hardware segments which can be operated in an overlapped fashion. The existing and many proposed pipelines assume that a task must flow synchronously, without wait or preemption, from segment to segment for its execution. In this paper we propose a pipeline model in which priority buffers are provided at every segment to control the flow of tasks. Several different priority implementations are analyzed assuming periodic arrivals of tasks. The characteristics studied are, queue size, wait time and throughput. It is shown that the theoretical maximum throughput of a pipeline is attainable with the use of internal buffers. Moreover, it is shown that a substantial degree of freedom in scheduling of tasks is achieved by these methods.
23 Aug 1978
TL;DR: BGRAF2 is a real-time interactive 2D graphics language that contends with an unusual combination of features: timing, events, parallelism, image manipulation, user interaction and procedural structures that creates many unpredictable interrelated tasks competing for execution.
Abstract: BGRAF2 is a real-time interactive 2D graphics language. Its supporting system contends with an unusual combination of features: timing, events, parallelism, image manipulation, user interaction and procedural structures. This combination creates within the system many unpredictable interrelated tasks competing for execution.A BGRAF2 program is compiled into an object module consisting of a sequence of pure code blocks, tasks, and a set of data blocks. The real-time environment is a hierarchical structure, where the highest level is a Scheduler, and the next level is composed of the object module and five additional processors: Graphics Processor, Control Processor, Input-Output Processor, Real-Time Processor and Memory Manager. The Scheduler is an abstract monitor responsible for scheduling tasks in accordance with a multi-level priority from a multi-queue scheme.
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: The parallel system (problem), computation history, concurrency matrix, scheduling discipline, and the history of parallel systems and computation history.
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: A computationally efficient procedure for treating n independent, single operation jobs, all available at time zero, on m identical processors, which utilizes human ingenuity to improve on a traditional solution procedure.
Abstract: Consider scheduling n independent, single operation jobs, all available at time zero, on m identical processors. Further, assume that each job must be processed by exactly one of these processors, and it is desired to minimize makespan. This paper reports a computationally efficient procedure for treating this problem, which utilizes human ingenuity to improve on a traditional solution procedure. Computational experience with the procedure indicates that good solutions to large problems are easily obtained; in fact out of 240 test problems, the optimal solution was found in every case. The entire procedure is simple enough for a shop foreman to be able to solve large problems by hand.
TL;DR: The main result, the average response time for a job conditioned on its service requirement, applies to a broad class of policy functions, including linear, exponential, and composite policy functions.
Abstract: This paper presents an analysis of time-sharing computer facilities using scheduling algorithms defined in terms of priority functions. We consider the class of algorithms in which a job's priority is defined by the difference between the time it spent in the system and an arbitrary function F of its attained service, where F is called the policy function. Our main result, the average response time for a job conditioned on its service requirement, applies to a broad class of policy functions. The derivation is based on the model of a processor-sharing M/G/1 queuing system and does not use transforms. The analysis is simplified by the decomposition of a non-Markovian process. Properties of the average response time resulting from policy function schedulers are discussed and related to those of other known time-sharing scheduling algorithms. For the examples of linear, exponential, and composite policy functions we plot the response times. We demonstrate the flexibility and the limitations of policy functions with respect to the discriminatory treatment of short jobs versus long ones and discuss the optimal selection of a policy function with respect to a given overall performance criterion.
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.