E. G. Coffman, Jr., Computer and Job Shop Scheduling Theory, Wiley, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....required to feasibly schedule a set of tasks by the Algorithm RMFF, and the minimum number of processors required to feasibly schedule the same set of tasks. Then 2.33. In order to prove the above bound, we define a function that maps the utilizations of tasks into the real interval [0, 1] as follows: or N 3 2 ( 1 ( u 2 2 1 ( 0 u 2 2 1 ( 1 2 2 1 ( u 1 = u f(u) 1.0 1 2 0 Figure 2: Mapping Function for RMFF and RMBF a=0.52 12 , where a = Let be k j tasks assigned to processor P j ....

....to the assumption that 1) Q.E.D. the RMBF Algorithm, and the minimum number of processors required to feasibly schedule the same set of tasks. Then 2. 33, where a = In order to prove the above bound, we define a function that maps the utilization of tasks into the real interval [0, 1] as it is done in the previous section. The function is the same as the one used for RMFF Algorithm. For a processor P j , its deficiency d j and its coarseness a j are similarly defined as those for RMFF Algorithm. Also note that Lemma 4.6, Lemma 4.7, and Lemma 4.8 also hold for those processors ....

E.G. COFFMAN, JR. (ED.), Computer and Job Shop Scheduling Theory, New York: Wiley, 1975.

....paths. As with the process of allocation, there are several strategies which can be implemented to improve the efficiency of this step. Parallel dynamic system simulation is often applicable to static task allocation methodologies. Classical allocation strategies, such as Critical Path Scheduling [10], Depth First Implicit Heuristic, DF IHS, method [11] and the HeavyNwA First,HN [12] algorithms, attempt to balance the amount of computation that occurs on each processing element while ignoring the effect of communication between processors. Other allocation methods are based solely upon ....

E. G. Coffman, Computer and Job-Shop Scheduling Theory, N w York: Wiley, 1976.

....of measuring execution time of a distributed application in a shared environment would be very desired. The need for eOEcient allocation of the activities (programs) to the resources (processors, communication channels) gave rise to many scheduling models in parallel processing (cf. monographs: [1, 3, 5, 6]) These deterministic scheduling models assume initial knowledge of the parallel application parameters such as processing times or communication delays. In this work we consider a method of obtaining these parameters, the precision and soundness of the nal model. The considerations of this work ....

E.G. Cooeman Jr. (editor). Computer and job-shop scheduling theory. Wiley & Sons, New York, 1976.

....of instruction scheduling may be more important, since these machines will feature longer memory latencies and more functional units. Despite the importance of scheduling, we know quite little about the behavior of list scheduling the most widely used technique for instruction scheduling [1, 3]. This paper presents an experimental evaluation of list scheduling that attempts to answer the following questions: 1. Is there room for improvement beyond list scheduling It is widely believed that list scheduling usually achieves optimal or near optimal results [5] is this the case 2. Will ....

Jr. E. G. Coffman, editor. Computer and Job-Shop Scheduling Theory. John Wiley and Sons, New York, 1976.

....2, s and range 0, 1, q . Recall that s is the number of processor classes anq q the number of distinct due times. Thus p = s# s: 0,1, s 0,1, q and s(k)s(k 1) 0k s . p defines the set of profile functions. Each profile function s defines a profile in a timing diagram (see [8]) i.e. the curve of t = d s(i) i = 1,2, s. We shall refer to the profile defined by s simply as the profile s. For example, consider the case s = 4, q = 5, and the profile function s such that s(0) s(1) s(2) 4; s(3) 2; and s(4) 1. Figure 2.1 displays s pictorially. Let s be a ....

E. Coffman, Jr., "Computer and job shop scheduling theory", John Wiley and Sons, Inc., New York, 1976.

....problem with committing to schedules is that they are computationally expensive to construct. The combinatorial complexity of the scheduling problem precludes an optimal solution, except for the most simple factory models [JM74] Gra81] In most realistic environments, the problem is NP complete [Cof76]. For example, where job changeover time is to be minimised, and where a fixed changeover time is given between every pair of adjacent jobs to be scheduled, the problem reduces to the travelling salesman problem [LM72] with m jobs represented by m cities and n processors represented by n ....

Coffman , E., ( Ed ), Computer and Job-shop Scheduling Theory, Wiley, 1976.

.... blocks that have been heavily optimized by a good optimizing compiler are small, and present little opportunity for finding instruction level parallelism [20] Even at the basic block level, finding an optimal solution to all but the simplest scheduling problems has been shown to be np complete [7]. In this work we will explore several aspects of instruction scheduling as they relate to modern processors and processor applications. We are interested in scheduling techniques that reduce static code size (in addition to execution time) and methods to combine instruction scheduling and ....

....Thus the techniques described in Section 5 may be applicable to one aspect of software pipelining. However that application is beyond the scope of this work. 2 List Scheduling The traditional way to schedule a basic block (and as we ll see later, larger program regions) is to use list scheduling [10, 15, 7]. The first step, is to build a data precedence graph (dpg) aka data dependence graph or ddg) for the block. The nodes of the graph are operations in the basic block, and the edges represent dependences between operations. An edge from node A to node B, means that node A must complete its ....

Jr. E. G. Coffman, editor. Computer and Job-Shop Scheduling Theory. John Wiley and Sons, New York, 1976.

.... West Lafayette, IN 47907 1285 USA Los Angeles, CA 90089 2560 USA alis, kim42 ecn.purdue.edu yangyu, gundala, gertphol, prasanna halcyon.usc.edu Colorado State University # Department of Electrical and Computer Engineering Department of Computer Science Fort Collins, CO 80523 1373 USA hj, aam colostate.edu Abstract Real time applications continue to increase in importance as they are employed in various critical areas, such as command and control systems. These applications have traditionally required custom made systems to execute them. Recently, with the ....

....when the applications are mapped in an on line fashion [36] e.g. when an increase in the workload of a system causes quality of service violations to occur [25, 44] or when new applications arrive unpredictably. Both types of mapping problems have been shown, in general, to be NP complete [13, 16, 26] Thus, the development of heuristic techniques to find near optimal mappings is an active area of research, e.g. 6, 5, 9, 10, 14, 17, 36, 38, 45] MSHN (Management System for Heterogeneous Networks) is a collaborative research effort among Colorado State University, Purdue University, ....

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E. G. Coffman, Jr. (ed.). Computer and Job-Shop Scheduling Theory. John Wiley & Sons, New York, NY, 1976.

....approach is used. Integer programming methods, on the other hand, allow for timing constraints. However, these constraints do not account for task queueing and intertask precedence constraints. Since the problem of assigning tasks subject to precedence constraints is generally NP hard [24], 25] 26] 27] some form of enumerative optimization or approximation using heuristics needs to be developed for this problem. For example, in [28] an enumeration tree of task scheduling is generated and searched using a heuristic algorithm called the CP MISF (Critical Path Most Immediate ....

E.G. Coffman, Computer and Job-Shop Scheduling Theory. New York: John Wiley & Sons, 1976.

....respects dependencies within programs. Each program being described as an arbitrary partial ordering of instructions. The precedence and resource constrained instruction scheduling problem has been studied well, and it is known that even by imposing restrictions, the problem is still NP hard [7] [17] 29] For example, when the execution times of tasks are not uniform and their partial order is arbitrary, then for two or more identical processing units, the problem of determining a minimal length, non preemptive schedule is NP complete [13] This result is true even if all of the tasks ....

....execution times for given applications on MAP architectures, an efficient (polynomialtime) scheduling algorithm based on one or a number of heuristics must be devised. 3. 1 The MAP Scheduling Problem List scheduling (LS) is a general method for scheduling tasks in resource constrained problems [7]. LS builds a ready set that contains all of the tasks which are not waiting on the results of other tasks. When a processor becomes available, a task with the highest priority is chosen from the set and assigned to it. The ready set is obtained from a topological sort of the data dependence ....

E. G. Coffman. Computer and Job-Shop Scheduling Theory. John Wiley and Sons, New York, 1976.

....and deployment of real time systems. In this dissertation, we address some aspects of the scheduling problem. Extensive literature exists on Job Shop and Flow Shop scheduling problems, in which a number of machines are scheduled to create complex parts and their assemblies [Pin95, Bru81, Cof76] We call such systems traditional systems to distinguish them from the real time systems that we study. A scheduling model for a real time system differs from a traditional scheduling model in the following ways: 1. Execution time variability In a traditional model, job execution times are ....

E. G. Coffman. Computer and Job-Shop Scheduling Theory, Ed. Wiley, New York, 1976.

....aim of the planning process is to find a schedule for processing all jobs to optimize one or more goals, for instance, minimizing mean flow time or mean tardiness. A variety of analytical models and optimization algorithms have been developed for solving static and dynamic deterministic problems [1 11]. Most efforts have been focused on two approaches: 1) developing optimization procedures and (2) designing new dispatching rules. The optimization approach [7,8,12] emphasizes a systematic exploration of all alternative schedules. In theory, it is possible to determine optimal schedules for ....

E. G. Coffman, J. L. Bruno, "Computer and job-shop scheduling theory", Wiley, New York, 1976.

....of the DEFs mapped to spilled registers and their uses in the un scheduled regions, so that spill load store OPs can be inserted in the DFG and carscheduled on the fly. 2. 4 The cars Algorithm The cars algorithm is given in figure 5, which is a modified version of the list scheduling algorithm [24]. In order to find the best cluster to schedule an OP, we first compute the resourceconstrained schedule cycle (lines 3 5 of figure 5) in which the OP can be scheduled in each cluster 7 Algorithm 1 cars: list scheduler version 1: while number of OPs in unscheduled 6= 0 do 2: select an Op from ....

E. G. Coffman, ed., Computer and job-shop scheduling theory. Wiley, New York., 1976.

....j i , V i t i V i T 2 i log T 2 i log W u i ( u i x i x i T i 1 T i = 1 Chapter 1 Introduction 1.1. Overview Scheduling problems occur in a variety of situations in which a set of resources is to be used to perform a set of tasks. The general problem of scheduling [11, 12] is to allocate resources for the performance of a set of tasks such that specified objectives are achieved. Examples of scheduling problems include (1) In summer Olympic Games, each game must be scheduled to take place at a certain site; some games are scheduled for the same site but for ....

....should be aware of how our problems relate to other problems that have been studied. To achieve these two goals, we offer a top down description of the problems and their relationship to other scheduling problems. A complete description of the general scheduling problem under various constraints [9, 12, 26], though desirable, is beyond the scope of this thesis. Generally, a scheduling problem is defined by four parameters: 1) the machine environment, 2) the task characteristics, 3) the scheduling environment, and (4) the scheduling objectives. The machine environment specifies the types of the ....

E.G. Coffman, Jr. (ed.), Computer and Job Shop Scheduling Theory, New York: 192 Wiley, 1975.

....the previous operation. The no wait scheduling environment is equivalent to a situation where this function increases very rapidly. 2 3 Useful General References Useful general references on machine scheduling problems include the books by Convey (1967) 25] Baker (1974) 20] Coffman (1976) [8], and French (1982) 7] Influential survey articles have been written by Gonzalez (1977) 9] Graham et al. 1979) 10] Lawler (1982) 17] Lawler at al. 1982) Lenstra and Rinnooy Kan (1985) 15] and Lawler at al. Callahan (1971) 21] describes a study of the steel industry, in which no wait ....

Coffman E. G. Computer And Job-shop Scheduling Theory. Wiley, New York, 1976.

.... costs on all assigned processors and interprocessor communications (IPC) costs, including graph theoretic solutions [132, 133] and integer programming solutions [84] among others [82, 84, 117, 124] Since the problem of assigning tasks subject to precedence constraints is generally NP hard [40, 50, 73, 77], some form of enumerative optimization or approximation us151 ing heuristics needed to be developed for this problem [36, 37, 66, 117] Ma et al. 84] and Sinclair [124] derived optimal task assignments to minimize the sum of task execution and communication costs with the branch and bound (B B) ....

E. G. Coffman, Computer and Job-Shop Scheduling Theory, Wiley and Sons, New York, 1976.

....processors not just some number of them. Hence, in the case of dedicated processors a multiprocessor task can be executed by a set of processors required simultaneously. Moreover, a task may be executed by some family of alternative processor sets. As it is in the classical scheduling theory [21, 37] multiprocessor tasks may consist of operations. In such a case we distinguish three types of dedicated processor systems: flow shop, open shop and jobshop. In the flow shop all tasks have the same number of operations which are performed sequentially and require the same sets of processors. In ....

....the set of tasks T consists of n tasks T 1 ; T n . For the whole task system it is possible to determine such features as preemptability (or nonpreemptability) and existence (or unexistence) of precedence constraints. These characteristics are defined as in the classical scheduling theory [21, 37]. A new feature is fixed or variable profile of a task. A profile of the multiprocessor task is fixed when the number (for parallel processors) or the set (for dedicated processors) of used processors does not change during the execution of the task. A profile is variable if it is possible to ....

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E.G.Coffman Jr. (editor), Computer and job-shop scheduling theory, John Wiley & Sons, New York, 1976.

....In the purely combinatorial version of our scheduling problem, the running times are known in advance, and the makespan is deterministic. If n is a deterministic state (i.e. n 0 = 0) then M(n) denotes the corresponding minimal makespan. The lemma below evaluates M(n) by applying Theorem 2. 1 in [2] which is due to T. C. Hu. It is also an easy extension of the results in [6] 3 and [8] we omit the details. Let knk = P k i=1 (k 1 Gamma i)n i denote the sum of the deterministic job lengths in n, and let [n] maxfk 1 Gamma ij1 i k; n i 0g denote a largest running time over all ....

E. G. Coffman, Jr., editor. Computer and Job-Shop Scheduling Theory. John Wiley and Sons, 1976.

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E. G. Coffman, Jr., Computer and Job Shop Scheduling Theory, Wiley, 1976.

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E. Coffman. Computer and Job-Shop Scheduling Theory. Wiley, New York, 1976.

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J. R. Coffman. 1976. Computer and Job-Shop Scheduling Theory. John Wiley, New Yo r k .

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Coffman, E.G. Computer and Job-Shop Scheduling Theory. John Wiley and Sons, New York, 1976.

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E.G. COFFMAN, JR. (ED.), Computer and Job Shop Scheduling Theory, New York: Wiley, 1975.

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E. G. Coffman Jr., Computer and Job Shop Scheduling Theory.New York: Wiley, 1976.

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E. G. Coffman, Jr. (ed.), Computer and Job-Shop Scheduling Theory, Wiley, New York, 1976.

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