G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE RTSS, pages 290--299, December 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....work: The early work of Dertouzos [8] showed that for underloaded systems, the Earliest Deadline First (EDF) strategy is 1 competitive. But in general, no O(1) competitive rm deadline scheduler exists; indeed, the best possible competitive ratio is (1 (Baruah et al. 2] Koren and Shasha [15]) To obtain better performance guarantees, one can allow online schedulers to use a faster processor. Speci cally, one compares an online scheduler that is given a faster processor but has no knowledge about the future against an o ine scheduler that uses only a unit speed processor but has ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318-339, 1995.

....of unit capacity. Even for this restricted model, called the parallel links model, we show that any deterministic online algorithm has a competitive ratio of at most 0. 66 (the bound holds for all k) The parallel links model is closely related to online preemptive task scheduling under overload [7, 6, 14, 15, 22, 20]. Our impossibility result applies to this problem as well. Our work extends previous work of Garay and Gopal [12] and Garay et al. 13] These papers also consider online bandwidth allocation with preemption on networks with line topology. However, they simplify the model by assuming that the ....

G. Koren and D. Shasha. D-over: An Optimal On-line Scheduling Algorithm for Overloaded Real-Time Systems. SIAM Journal on Computing, Vol. 24, pages 318--339, 1995.

....value of jobs meeting the deadlines. Preemption is allowed at no cost (i.e. a preempted job can be restarted from the point of preemption at any time) The o line version of this problem is known to be NPhard and the on line version has been studied intensively over the last decade (see, e.g. [1, 9, 10]) The design of a good scheduler is further complicated by the fact that jobs may have di erent value densities, i.e. di erent ratios of value to processing time. The importance ratio k of a system is de ned as the ratio of the largest possible value density to the smallest possible value ....

....if it can always match the optimal o line algorithm on the total value obtained. It has been known for long that no on line algorithm for rm deadline scheduling [6] can be 1 competitive, and the best known algorithm achieves a competitive ratio of ( where k is the importance ratio [10]. In recent years, a plausible approach to studying performance guarantee of on line algorithms (without making assumption on future inputs) is to allow on line schedulers to have faster processors (e.g. 4, 7, 9, 14, 8, 12, 13] Speci cally, we would like to compare on line schedulers using a ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal of Computing, 24(2):318-339, 1995.

....can be 1 competitive; indeed, Baruah et al. 2, 3] gave a lower bound of (1 on the competitive ratio, where k is the importance ratio. That means, even if all jobs have uniform job density (i.e. k = 1) the best algorithm we can expect is 4 competitive. Afterward, Koren and Shasha [13] showed that this lower bound is tight by giving a (1 competitive algorithm. Notice that when k is large, such performance guarantee is not satisfactory. In recent years, a plausible approach to obtaining better performance guarantee without making assumption on future inputs is to allow ....

....0.01 0.1 0.5 1 2 10 speed 1.02 1.2 2 3 5 21 (1 ) 123321 648.4 32.0 12 5.65 2.05 40201 421 21 7 3 1.24 Table 1: The rst row illustrates the competitive ratio of Slacker given in [10] the second row shows our new result. ratio can be improved from 4 (due to the result in [13]) to 2 using two unit speed processors, and in general to p= p 1) with p processors. Second, if the concern is to maximize the total number of job completions, Kalyanasundaram and Pruhs [9] gave an algorithm that is O(1) competitive when given two unit speed processors. In this paper, we revisit ....

Gilad Koren and Dennis Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318 339, April 1995.

....0 if, for any job sequence, A can attain at least a fraction 1=c of the total value obtained by any o line algorithm [4] Furthermore, A is said to be speed s c competitive if A is allowed to use processors s times faster than the o line adversary. In the single processor setting, Koren and Shasha [12] have given a (1 k) competitive algorithm, where k is the importance ratio. Kalyanasundaram and Pruhs [10] later showed that a speed O(1) processor is su cient to improve the competitive ratio to a constant. In particular, their algorithm is speed 2 32 competitive. In the multiprocessor ....

Gilad Koren and Dennis Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318 339, April 1995.

....for underloaded systems, the Earliest Deadline First (EDF) strategy is optimal. But in general, no optimal or O(1) competitive rm deadline scheduler can be constructed; indeed, the best competitive ratio has a matching upper bound and lower bound of (1 (Baruah et al. 2] Koren and Shasha [14]) To obtain better performance guarantee, we allow online schedulers to use a faster processor. Speci cally, we compare an online scheduler that is given a faster processor but has no knowledge about the future against an o ine scheduler that uses only a unit speed processor but has complete ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318-339, 1995.

....algorithm that can guarantee to attain more than one fourth of the processor utilization of the optimal offline algorithm. Another way to express this result is that the competitive ratio of any on line algorithm is at least 4. This lower bound is tight as matching algorithms are also known [1, 9, 14]. In recent years, there are a number of exciting results on improving performance guarantee without making assumption on future inputs; the basic idea is to allow the online scheduler to have more resources than the adversary (e.g. 3, 6 8, 10 12] For the single processor deadline ....

Gilad Koren and Dennis Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318--339, April 1995.

....1 competitive if it can always match the optimal o line algorithm on the total value obtained. It has been known for long that no on line algorithm for rm deadline scheduling [5] can be optimal, and the best known algorithm achieves a competitive ratio of ( where k is the importance ratio [9]. In recent years, there are a number of exciting results on improving the performance guarantee without making assumption on future inputs; the basic idea is to allow the on line scheduler to have more resources than the adversary (e.g. 3, 6, 8, 13, 7, 11, 12] For the single processor rm ....

....rm deadline scheduling problem, Kalyanasundaram and Pruhs [8] showed that the competitive ratio can be reduced signi cantly if the on line scheduler is given a faster processor. For instance, with a processor that is 32 times faster, the competitive ratio can be improved from ( [9] to roughly 2. Recently, Lam and To [12] proved that even optimality can be achieved. Precisely, they showed that the earliest deadline rst (EDF) algorithm is optimal when given a processor that is 4 dlog ke times faster; for the special case where k = 1, a processor that is two times faster ....

Gilad Koren and Dennis Shasha. D over : An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal of Computing, 24(2):318-339, April 1995.

....not match our requirements because of their sharp decrease. As a result of the rm deadline, the real time scheduling model is hard to approximate. The optimal deterministic competitive ratio for the uniprocessor case is ( where is the ratio between the maximum and minimum bene t densities [3, 4, 7]. For the special case where = 1, there is a 4 competitive algorithm. The optimal randomized competitive ratio for the uniprocessor case is O(min(log ; log ) where is the ratio between the longest and shortest job [6] For the multiprocessor case, Koren and Shasha [8] showed that when the ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for over-loaded real-time systems. IEEE Real-time Systems Symposium, pages 290-299, 1992.

....systems [34] pioneered by the Spring kernel project [35, 36] was introduced later to describe applications where runtime workload is unknown until admission control time. It resulted in innovative planning based scheduling algorithms that provide online guarantees for dynamically arriving tasks [18, 25, 28, 33, 37, 43, 44]. Task execution times where assumed to be known, e.g. using pre run time code analysis techniques such as [15, 38, 42] The results of the analysis depend on specific platform hardware and operating system. The analysis, therefore, needed to be repeated for each target platform. With the advent ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE Real-Time Systems Symposium, pages 290--299, Phoenix, Arizona, December 1992.

....scheduling problems that we study, we can then ask what competitive ratio can be achieved for a given speed up factor s, or what speed up is necessary if possible at all to achieve 1 competitiveness. The standard model. This problem has been extensively studied. As shown by Koren and Shasha [6], in this model it is possible to achieve the competitive ratio of ( p 1) 2 , where = max j w j = min j w j is called the importance factor. This ratio is in fact optimal [1, 6] Since no constant competitive algorithms in this model are possible, it is natural to study this problem ....

....1 competitiveness. The standard model. This problem has been extensively studied. As shown by Koren and Shasha [6] in this model it is possible to achieve the competitive ratio of ( p 1) 2 , where = max j w j = min j w j is called the importance factor. This ratio is in fact optimal [1, 6]. Since no constant competitive algorithms in this model are possible, it is natural to study this problem under the resource augmentation framework. Kalyanasundaram and Pruhs [4] present an online algorithm that uses a processor with speed 32 and achieves a constant competitive ratio. Lam and To ....

G. Koren and D. Shasha. d over : an optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24:318-339, 1995.

....up a machine to handle a job for one web site if it handled a job in the previous time unit for a di erent site. Several papers have considered the problem of throughput maximization in scheduling jobs on parallel machines with release times and deadlines, both in the o ine and online settings [5, 3, 7, 8, 14]. In the standard notation, this type of problem is denoted by P jr i j P w i (1 U i ) The type of setup considered here is related to batch setup scheduling, for which several o ine problems have been studied (see [17] for a survey) The online problems considered here also relate to ....

G. Koren and D. Shasha, \D-over: An optimal on-line scheduling algorithm for overloaded real-time systems". SIAM Journal on Computing, 24 (1995), pp. 318-339.

....more general on line problem where the processing time is not fixed was considered in [16] In this case the results are substantially worse than our case. Slightly better results can be achieved for the case where processing time is not fixed if preemption is allowed. This case was considered in [5, 6, 12]. For the unweighted version of this problem, i.e. when the goal is to maximize the number of jobs completed by their deadline (which is trivial in case all processing times are the same) 5] showed a tight competitive factor of 4. For the weighted version the bound is p 1 k 2 where k is ....

....the number of jobs completed by their deadline (which is trivial in case all processing times are the same) 5] showed a tight competitive factor of 4. For the weighted version the bound is p 1 k 2 where k is the ratio of the maximum value density to the minimum value density of a job [12]. Paper organization. The remainder of this paper is organized as follows. In Section 2 we define the models and some notation. In Section 3 we consider the FIFO model, and in Section 4 we consider the bounded delay models. Finally in Section 5 we discuss off line algorithms. Due to lack of ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal on Computing, 24:318--339, 1995.

....count (CC) Informally, EPU measures the fraction of time during overload that the processor spends on executing tasks that will complete by their deadlines, while CC measures the number of tasks executed to completion during the overload interval. To the best of our knowledge, previous work [2, 14, 3, 9, 15] focused on the case when EPU is the measure of scheduling performance. Some algorithms have also been proposed to deal with overloads that improve the performance of EDF that is optimal when system is underloaded [2, 8, 11] Baruah et al. 13] have shown that there exists an upper bound on the ....

G. Koren, D. Shasha. d over : An optimal on-line scheduling algorithm for overloaded realtime systems. In Proceedings of 13th Real-Time Systems Symp., December 1992.

.... no mechanism is provided to specify the number of tolerable task instances or their failure distribution (Spuri, Buttazzo, Sensini, 1995) As a forerunner to their work Koren et al. introduced a skip factor for skipping one out of a set of task invocations in order to reduce a system overload (Koren and Shasha, 1992). None of these contributions deals with hard deadlines or unpredictable task arrival. Organization of the Paper. In section 2 a stepwise introduction of criticality, sensitivity and similarity of transaction instances will be given, based on the corresponding concepts for task instances. This ....

Koren, G., D. Shasha (1992). D-over: An Optimal On-line Scheduling Algorithm for Overloaded Real-Time Systems. Proceedings 13 th IEEE Real-Time Systems Symposium, Phoenix, Arizona, USA, December 1992,pp.290-300.

.... no mechanism is provided to specify the number of tolerable task instances or their failure distribution (Spuri, Buttazzo, Sensini, 1995) As a forerunner to their work Koren et al. introduced a skip factor for skipping one out of a set of task invocations in order to reduce a system overload (Koren and Shasha, 1992). None of these contributions deals with hard deadlines or unpredictable task arrival. Similarity of objects and similarity of tasks have been introduced through different concepts (Kuo and Mok, 1992; Chen and Mok, 1997) Object and task similarity had been combined and interrelated in a new way ....

Koren, G., D. Shasha (1992). D-over: An Optimal On-line Scheduling Algorithm for Overloaded Real-Time Systems. Proceedings 13 th IEEE Real-Time Systems Symposium, Phoenix, Arizona, USA, December 1992,pp.290-300.

....more general on line problem where the processing time is not xed was considered in [16] In this case the results are substantially worse than our case. Slightly better results can be achieved for the case where processing time is not xed if preemption is allowed. This case was considered in [5, 6, 12]. For the unweighted version of this problem, i.e. when the goal is to maximize the number of jobs completed by their deadline (which is trivial in case all processing times are the same) 5] showed a tight competitive factor of 4. For the weighted version the bound is p 1 k 2 where k is ....

....the number of jobs completed by their deadline (which is trivial in case all processing times are the same) 5] showed a tight competitive factor of 4. For the weighted version the bound is p 1 k 2 where k is the ratio of the maximum value density to the minimum value density of a job [12]. Paper organization. The remainder of this paper is organized as follows. In Section 2 we de ne the models and some notation. In Section 3 we consider the FIFO model, and in Section 4 we consider the bounded delay models. Finally in Section 5 we discuss off line algorithms. Due to lack of space, ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal on Computing, 24:318339, 1995.

.... begun investigating the impact of overload with respect to CC, and an initial set 2 0 0 1 4 10 3 8 TASK T1 TASK T2 time Figure 1: Effective Processor Utilization (EPU) EPU metric has been widely used in the analysis of real time scheduling algorithms under conditions of overload (e.g. [15, 4, 3, 13, 17]) A detailed discussion of the applicability of this metric to real time systems is provided in [15] In particular, our goal is to compare the EPU performance of on line scheduling algorithms against that of an optimal off line (or clairvoyant) algorithm. On line schedulers make scheduling ....

....algorithms are based on heuristics, pathological conditions exist where their performance can be arbitrarily poor; they cannot, therefore, provide any worst case guarantee on EPU performance. Of late, there has been considerable activity in theoretical studies of overload scheduling algorithms [3, 4, 13, 8]. A common feature of these studies is that they all consider work4 loads where tasks can have arbitrary slack factors. In contrast, our study investigates the performance improvement that can be realized for workloads where all tasks are guaranteed to have a pre specified minimum slack factor. ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded real-time systems. In Proc. of the 13th Real-Time Systems Symposium, Phoenix, Arizona, December 1992. IEEE Computer Society Press.

....which is 1=k of the capacity of the link for some integer k. Even for this restricted model we show that any deterministic on line algorithm has a competitive ratio of at most 0:66 (the bound holds for all k) Our model is closely related to on line preemptive task scheduling under overload [7, 6, 13, 14, 19, 18]. Our impossibility result applies to this problem as well. Our work extends previous work of Garay and Gopal [11] and Garay et al. 12] These papers also consider on line bandwidth allocation with preemption on networks with line topology. However, they greatly simplify the model by assuming ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded real-time systems. TR 594, Courant Institute, New York University, 1992. 18

....completed before their deadlines. For this more general setting, there are several online algorithms in the literature. These algorithms are not optimal, though. De ne the value density of a job to be the ratio of its value to its required work. In the single processor setting, Koren and Shasha [8] generalized the work of Koren et al. 1] to give an (1 p k) 2 competitive 2 algorithm, where jobs are assumed to have value density in the range [1; k] Kalyanasundaram and Pruhs [7] gave another algorithm called Slacker, which is O(1) competitive when a faster processor is used. ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. Comput., 24(2):318339, 1995.

....the Spring kernel project [36, 37] introduced the third major paradigm to describe applications where run time workload parameters are unknown until admission control time. It resulted in innovative planning based scheduling algorithms that provide online guarantees for dynamically arriving tasks [17, 25, 28, 34, 38, 46, 47]. Task execution times where assumed to be known, e.g. using pre run time code analysis techniques such as [14, 39, 45] With the advent of a new category of soft real time applications such as multimedia, real time databases, and e commerce, the concept of QoS adaptation was introduced into ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE Real-Time Systems Symposium, pages 290--299, Phoenix, Arizona, December 1992.

....any guarantee on the number of deadlines a task may miss. They also assume that all tasks have the same m, k parameters. They use the concept of (m; k) rm deadlines as a desired level of service as opposed to a guaranteed level of service. Another approach is the introduction by Koren and Shasha [12] of the skip factor, s. If a task has a skip factor of s it will have one invocation skipped out of s. They introduce the D over dynamic priority scheduling algorithm which is based on deciding which task invocations to skip. Later in [10] the same authors introduce two scheduling algorithms for ....

....hard constraints Met deadlines Missed deadlines Any order n m n m Consecutive n m hni These constraints model other notations introduced previously by other researches. For instance, the notion of (m; k) rm deadlines [11] maps directly to the m k constraint. The skip factor s [12] maps to the 1 s 1 or s s 1 . 3.4 Weakly hard constraints for repeating tasks Up to now, we have only considered weakly hard constraints for periodic tasks. However, these constraints can not be applied directly to non periodic tasks. There are essential di erences between periodic ....

G. Koren and D. Shasha, \D-over: An optimal on-line scheduling algorithm for overloaded real-time systems," in proc. 13th IEEE Real-Time Systems Symposium, Phoenix, Arizona, USA, December 1992, pp. 290-300.

....lvj would prevent the overload, then it checks whether value Gamma density (lvj) value Gamma density (lvdj) expected Gamma utility (lvj) expected Gamma utility (lvdj) If this inequality holds, BE v removes lvdj; otherwise BE v removes lvj. The intuition follows from the D over [KS92] algorithm: to determine which job 5 We term them teasers because their value density is very high, due to the small CPU requirements. to abort one must consider not only value densities but also the ratios of the value densities and expected values; the latter is used to determine if a higher ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In RealTime Systems Symposium. Phoenix, AZ, 1992.

....of unit capacity. Even for this restricted model, called the parallel links model, we show that any deterministic online algorithm has a competitive ratio of at most 0. 66 (the bound holds for all k) The parallel links model is closely related to online preemptive task scheduling under overload [7, 6, 14, 15, 22, 20]. Our impossibility result applies to this problem as well. Our work extends previous work of Garay and Gopal [12] and Garay et al. 13] These papers also consider online bandwidth allocation with preemption on networks with line topology. However, they greatly simplify the model by assuming ....

G. Koren and D. Shasha. D-over: An Optimal On-line Scheduling Algorithm for Overloaded Real-Time Systems. SIAM Journal on Computing, Vol. 24, pages 318--339, 1995.

....on temporal query processing, and [15] which is one of the very few papers that we are aware of, on temporal transaction processing. RTDBSs have seen substantial research effort as well in recent years. Much of this effort has been focussed towards developing high performance scheduling algorithms [1, 2, 14, 21, 25, 31, 37] as well as concurrency control algorithms [6, 22, 24, 26, 27, 33] Typically, performance has been characterized as the ability to reduce transaction tardiness. None of this work has been performed with temporal consistency in mind. Even though not much is reported on the confluence of temporal ....

G. Koren and D. Shasha. D over : An optimal On-Line Scheduling Algorithm for Overloaded Real-Time Systems. In Proceedings of the IEEE Real-Time Systems Symposium, pages 290-- 299, August 1992.

....lvj would prevent the overload then check if value Gamma density (lvj) value Gamma density (lvdj) expected Gamma utility (lvj) expected Gamma utility (lvdj) If this holds BE v removes lvdj; otherwise BE v removes lvj. The intuition behind this heuristic follows from the D over [KS92] algorithm: to determine which job to abort one must consider not only value densities but also the ratios of the value densities and expected values; the latter is used to determine if a higher value job should be aborted in favor of a higher value density job. As an example, suppose the queue ....

....what deliberation to perform, and for integrating new information about changes in the world. The capabilities were all required, at least in primitive form, before we could use the deliberation scheduling algorithms in DIPART. Our experiments showed that BE v scheduling (and probably D over [KS92] appears to be an especially promising algorithm for the deliberation scheduling problem, when value, deadline, and computation times are available or can be estimated and when the decay function used is exponential. BE schedulers are based on a heuristic and it is easy to come up with ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded realtime systems. In Real-Time Systems Symposium. Phoenix, AZ, 1992.

....short transactions may have long deadlines) Also, as we show in section 5, under overload, the performance of AEVD deteriorates rather sharply. Though this deterioration is slower than the dramatic performance degradation of ED, it is still 1 We ascribe similar meaning to system loading as in [13]: a system is underloaded if there exists a schedule that will meet the deadline of every task and overloaded otherwise. very significant. Consequently, the area of overload management remains very much an open area of research. 1.3 Contributions of This Paper Given that overload management is ....

G. Koren and D. Shasha. D over : An optimal On-Line Scheduling Algorithm for Overloaded Real-Time Systems. In Proceedings of the IEEE Real-Time Systems Symposium, pages 290-- 299, August 1992.

....is not much work at all on the synthesis of these fields, which is what this paper proposes. There has been substantial research efforts devoted to Real Time database Systems (RTDBSs) in recent years. Much of this effort has been focussed towards developing high performance scheduling algorithms [1, 2, 22, 25, 31, 12, 34] as well as concurrency control algorithms [21, 26, 27, 24, 23, 32] For a nice discussion on the requirements of RTDBSs see [20] and for a nice survey of recent work see [48] Typically, performance has been characterized as the ability to reduce transaction tardiness. None of this work has been ....

G. Koren and D. Shasha. D over : An optimal On-Line Scheduling Algorithm for Overloaded Real-Time Systems. In Proceedings of the IEEE Real-Time Systems Symposium, pages 290-- 299, August 1992.

....would prevent the overload then checks the inequality value Gamma density (lvj) value Gamma density (lvdj) expected Gamma utility (lvj) expected Gamma utility (lvdj) and if true BE v removes lvdj; otherwise BE v removes lvj. The intuition behind this heuristic follows from the D over [KS92] algorithm: to determine which job to abort one must consider not only value densities but also the ratios of the value densities and expected values; the latter is used to determine if a higher value job should be aborted in favor of a higher value density job. For example, suppose the queue ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In Real-Time Systems Symposium. Phoenix, AZ, 1992.

....handle. We present a simple algorithm for use in overload mode that seeks to avoid very bad behavior. We focus most of our attention on scheduling in normal mode. The focus of this paper is therefore somewhat different than that of most work involving overloaded systems (e.g. B 91, BS89, KS92, Loc86, SLR86, SZ92, TWW87] rather than focusing on dealing with overload once it occurs, we focus on dealing with the potential for overload before it actually occurs. For normal mode we would like an algorithm that tries to meet al..l deadlines, while at the same time avoiding the need to enter ....

....set. Alternatively, we might seek to maximize the total number of tasks that meet their deadlines, or we might associate a value to each task and try to maximize the total value of completed tasks. Much research has been done toward approaching these or similar goals (see, e.g. B 91, BS89, KS92, Loc86, SLR86, SZ92, TWW87] and it appears that more research is needed. We will content ourselves here with suggesting a straightforward algorithm that is relatively easy to implement and seeks to avoid wasting time on tasks that will not complete. Because the system is overloaded, we would ....

G. Koren and D. Shasha. D over : an optimal on-line scheduling algorithm for overloaded real-time systems. In Proc. 13th IEEE Real-Time Systems Symp., pages 290--299, 1992.

....of the link for some integer k. Even for this restricted model we show that any deterministic on line algorithm has a competitive ratio of at most 0:66 (the bound holds for all k) This model is closely related to on line preemptive task scheduling under overload [BKM 91b, BKM 91a, KS92, WM91, SWW91] Our impossibility result applies to this problem as well. Our work extends previous work of [GG92, GGK 93] These papers also consider on line bandwidth allocation with preemption on line networks. However, they greatly simplify the model by assuming that the bandwidth ....

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded real-time systems. Technical Report 594, Courant Institute, New York University, 1992.

....temporal transaction processing, is a very open problem which has been recognized as being important. Real Time database Systems (RTDBSs) have seen substantial research effort as well in recent years. Much of this effort has been focussed towards developing high performance scheduling algorithms [1, 2, 35, 38, 44, 21, 50] as well as concurrency control algorithms [8, 34, 39, 40, 37, 36, 46] For a nice discussion on the requirements of RTDBSs see [33] and for a nice survey of recent work see [73] Typically, performance has been characterized as the ability to reduce transaction tardiness. None of this work has ....

G. Koren and D. Shasha. D over : An optimal On-Line Scheduling Algorithm for Overloaded RealTime Systems. In Proceedings of the IEEE Real-Time Systems Symposium, pages 290--299, August 1992.

....on temporal query processing, and [15] which is one of the very few papers that we are aware of, on temporal transaction processing. RTDBSs have seen substantial research effort as well in recent years. Much of this effort has been focussed towards developing high performance scheduling algorithms [1, 2, 21, 25, 31, 14, 37] as well as concurrency control algorithms [26, 27, 24, 22, 6, 33] Typically, performance has been characterized as the ability to reduce transaction tardiness. None of this work has been performed with temporal consistency in mind. Even though not much is reported on the confluence of temporal ....

G. Koren and D. Shasha. D over : An optimal On-Line Scheduling Algorithm for Overloaded Real-Time Systems. In Proceedings of the IEEE Real-Time Systems Symposium, pages 290-- 299, August 1992.

....working if it is to be successful, and a computation time, the time it actually needs in order to run in its entirety. Each task has a value obtained if completed successfully. The special case where the value of a task is proportional to its running time is called the Uniform Value Density case [3, 10]. The aim of the system is to maximize the sum of the values obtained from all successfully completed tasks. It is the duty of the scheduler to schedule the tasks that maximize this total value. A number of issues are raised at this point. A scheduler that knows in advance all the tasks and ....

.... schedule that allows all tasks to successfully complete, there exist on line schedulers with 100 guarantee [6] In the overloaded case such an optimal schedule is impossible [11] Scheduling algorithms such as D over give a competitive guarantee for overloaded firm real time systems [10]. In this paper we are concerned with multiprocessor real time systems with preemption. Mok and Dertouzos [7] showed that even in an underloaded system, no on line algorithm can guarantee 100 success. A task is said to migrate if it continues running on a different processor from the one it was ....

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G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for over-loaded real-time systems. SIAM J. Computing, 24(2):318--339, 1995.

....a lower bound of (1 p k) 2 . Wang and Mao [12] first reported an algorithm that achieves this bound when k is 1. Having independently developed an algorithm for the k = 1 case, we were able to generalize this to an algorithm called D over that meets the Baruah et al. bound for all k [7]. For multi processor environments, Mok and Dertouzos [4] showed that no optimal algorithm exists even when the system is underloaded. Locke ( 9] pp. 124 134) presented heuristics for this case. 1 Finding the maximum achievable value for such a scheduler, even in the uniprocessor case, is ....

....details of these algorithms and their analysis, these can be found in appendix A at the end of this paper. 15 Tasks may have slack time. 7 Conclusion number of importance bounds processors ratio complexity algorithmic comments 1 : any k 1 (1 p k) 2 tight tight bound achieved by D over [7]. 2 : 1 2 tight tasks have no slack time and may not migrate between processors [3,12] 2 : 1 2 3 z tasks may have slack time but may not migrate between processors. 2 : 1 2 tight z tasks may have slack time and may migrate between processors. n : k 1 k (k Gamma1) n(k 1 n Gamma 1) z ....

G. Koren, D. Shasha. D-over: An Optimal On-Line Scheduling Algorithm for Overloaded RealTime Systems, In Proc. of 1992 IEEE Real-Time Systems Symposium , Phoenix, Arizona, pp. 290-299, December 1992.

....is given no information about a task before its release time. When a task is released, its value, computation time and deadline are known precisely. If a task completes before its deadline, then the system acquires its value. Otherwise, the system acquires no value for that task. Following [8, 13], we denote such deadlines as firm. Other papers [4] denote such deadlines as hard. 1 A reasonable assumption since real time kernels are designed to keep all tasks code and data in memory thereby avoiding paging induced faults during context switches; also, such kernels are built with short ....

....scheduling algorithm (also called an off line scheduler) A clairvoyant scheduler has complete a priori knowledge of all the parameters of all the tasks. A clairvoyant scheduler can choose a scheduling sequence that will obtain the maximum possible value achievable by any scheduler 3 . As in [3, 9, 13, 19] we say that an on line algorithm has a competitive factor r; 0 r 1, if and only if it is guaranteed to achieve a cumulative value of at least r times the cumulative value achievable by a clairvoyant algorithm on any set of tasks. For convenience of notation, we use competitive multiplier as ....

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G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In Proceedings of the 13th Real-Time Systems Symposium, pages 290--299, Phoenix, Arizona, Dec. 1992. IEEE.

....multiplier that any on line scheduler can have. Wang and Mao [2, 21] first reported an algorithm that achieves this bound when k is 1. Having independently developed an algorithm for the k = 1 case [12] we were forced to use a different algorithmic strategy to achieve an algorithm called D over [11, 13] that meets the Baruah et al. bound for all k. For multiprocessor environments, Wang and Mao [2, 21] showed a lower bound of 2 (on the competitive multiplier) and presented an algorithm that achieved this bound for an arbitrary even number of processors, assuming uniform value density and that ....

....adversary arguments and algorithms offer two useful insights: 1. A parallel on line scheduling algorithm achieves a competitive guarantee by allocating some processing resources according to tasks value density. This is a qualitative difference from our uniprocessor scheduling algorithm D over [11, 13] which made its decisions based on total value only. Moreover, high value density tasks in the MOCA Algorithm have priority over lower value density tasks in the sense that they have more processors on which they can be scheduled due to the cascading. 2. The lower bound on the best possible ....

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal on Computing. to appear.

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G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE RTSS, pages 290--299, December 1992.

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G. Koren and D. Shasha, D-over: An optimal on-line scheduling algorithm for overloaded real-time systems, SIAM Journal of Computing 24 (1995), no. 2, 318--339.

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G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318-339, 1995.

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Gilad Koren and Dennis Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24(2):318-- 339, April 1995.

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G. Koren and D. Shasha. d over : an optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24:318-339, 1995. 17

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G. Koren and D. Shasha, D-over: An optimal on-line scheduling algorithm for overloaded realtime systems, SIAM Journal of Computing 24 (1995), no. 2, 318--339.

No context found.

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE Real-Time Systems Symposium, pages 290--299, Phoenix, Arizona, December 1992. 33

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G. Koren and D. Shasha. d over : an optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24:318-339, 1995.

No context found.

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. Comput., 24(2):318--339, 1995.

No context found.

G. Koren and D. Shasha. D over : An optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM J. Comput., 24(2):318--339, 1995.

No context found.

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. In IEEE Real-Time Systems Symposium, pages 290--299, Phoenix, Arizona, December 1992. 33

No context found.

G. Koren and D. Shasha. d over : an optimal on-line scheduling algorithm for overloaded uniprocessor real-time systems. SIAM Journal on Computing, 24:318-339, 1995. 17

No context found.

G. Koren and D. Shasha. D-over: An optimal on-line scheduling algorithm for overloaded real-time systems. SIAM Journal on Computing, 24:318-339, 1995.

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