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can be considered as having an unlimited number of processors, because the task execution is nonpreemptive (Property 2 of De nition 43 of the target system model) and only entire tasks are scheduled Hence, if there are more processors than nodes, the surplus processors will have no tasks to execute and can be removed from the system without in uencing the schedule Theorem 42 (NP-Completeness Unlimited Number of Processors) Let G = (V, E, w, c) be a task graph and P a parallel system, with |P | |V| The decision problem SCHED(G, P ) associated with the scheduling problem is as follows Is there a schedule S for G on P with length sl(S) T , T Q+ SCHED(G, P ) is NP-complete The proof for this theorem can be based on a reduction from PARTITION, as mentioned earlier, and is left as an exercise for the reader (Exercise 43) As a logical consequence of the NP-completeness of scheduling, the scienti c community has been eager to investigate ef cient scheduling algorithms based on heuristics or approximation techniques that produce near optimal solutions In practice, task scheduling must rely on these algorithms due to the intractability of the problem In the following chapters, many task scheduling algorithms are analyzed, whereby the focus is on common techniques encountered in many algorithms This section nishes with a simple lemma regarding the optimal schedule length and the number of processors In general, the more processors are available for the task graph to be scheduled on, the smaller (or equal) the optimal schedule length (Darte et al [52]) Lemma 42 (Relation Available Processors Schedule Length) Let G = (V, E, w, c) be a task graph and P, P+1 two parallel systems with the only difference



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have been two basic approaches: self-similar (fractal) processes and uid renewal models with long-tailed renewal distributions In this presentation we focus on the latter The investigation of queueing systems with self-similar arrival processes can be found in the literature [23, 24, 44, 47, 49, 51, 54, 55] In this chapter some recent results are presented on the subexponential asymptotic behavior of queueing systems with subexponential arrival streams The related references will be listed throughout the chapter First, in Section 102 the classes of long-tailed and subexponential distributions are de ned and some of their basic properties are presented Section 103 begins with a presentation of a classical result on the subexponential asymptotics of a GI =GI =1 queue That is followed by a brief discussion of various extensions of this result that can be found in the literature The remainder of Section 10.





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Asprise Java OCR library offers a royalty-free API that converts images (in formats like JPEG, PNG, TIFF, PDF, etc.) into editable document formats Word, XML, ...

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3 contains two new results on this subject In Section 1031 a derivation is given for a straightforward asymptotic approximation for the loss rate in a nite buffer GI =GI =1 queue It appears surprising that the derived asymptotic formula does not depend on the queue service process However, a simple intuitive explanation of this insensitivity effect is provided In Section 1032 a GI =GI =1 queue with truncated heavy-tailed arrival sequences is analyzed Explicit asymptotic characterization of a unique behavior of the queue length distribution is given Informally, this distribution on the log scale resembles a stair-wave function that has steep drops at speci c buffer sizes This has important design implications, suggesting that negligible increases of the buffer size in certain buffer regions can decrease the over ow probabilities by orders of magnitude Section 10.

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4 describes a class of uid queues and addresses the problem of multiplexing on=off sources with heavy-tailed on periods A complete rigorous treatment of the subexponential asymptotic behavior of a uid queue with a single on=off arrival process is presented in Section 1041 Section 1042 investigates multiplexing a heavy-tailed on=off process with a process that has a lighter (exponential) tail It is shown that this queueing system is asymptotically equivalent to the queueing system in which the process with the lighter tail is replaced by its mean value This has implications on multiplexing bursty data and video traf c with relatively smooth voice sources Section 1043 addresses the problem of multiplexing on=off sources with heavy-tailed on periods Understanding of this problem is fundamental for achieving high network resource utilization and providing quality of service in the bursty traf c environment.

that |P+1 | = |P| + 1 For the optimal schedule of G on the two systems, it holds that sl(Sopt (P+1 )) sl(Sopt (P)) (415)

Under a speci c stability condition this problem admits an elegant asymptotic solution A brief conclusion of the presentation is given in Section 105..

system Finally, for a multiple-state arrival process, we may further limit the analysis to an arbitrary single state of the arrival process and compare transient performance measures computed under different modeling assumptions With this approach, we have gained some insights into QoS impact of long-range dependence in network traf c The rest of the chapter is organized as follows In Section 132, we rst introduce a framework for traf c modeling that captures the essential property of long-range dependence Within this framework, traf c is modeled by multistate, uid-type stochastic processes When such a process is in a given state, the underlying traf c source generates traf c at a constant rate The time spent by the process in a state is a random variable For the purpose of this chapter, we let the distribution of the random variable be arbitrary.

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tesseract ocr in java

Using Tesseract OCR to extract scanned invoice data in Java web ...
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OCR with Java and Tesseract – Brandsma Blog
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