M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497--1506, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for real time applications. However, the programming of such multiprocessor systems presents a rather formidable probIem. In particular, time critical tasks must be serviced within certain preassigned deadlines dictated by the physical environment in which the multiprocessor system operates [1]. Thus, efficient methods and tools for allocation and scheduling of tasks are needed. In general, a task can be characterized by an integer triple (S, C, D) where S is the start time of the task, C is the execution time of the task, and D is the deadline. A precedence relation may be defined on ....

....PAi[n] and PI = Psl[l] Psl[n] be chromosomes A and B of parent PI, and Pa2 and Pa2 be chromosomes A and B of parent P2, respectively. Then, generate a crossover point k randomly, l k n. 2) The left segments of CA1 and Ci of the child C1 are CA1 : PAl[l] PAl[k] and Csl : Psl [1] . Pl[k] 3) Scan the parent string Pa2 from left to right for P,2[t] such that PA2[i] CA 1 [j] for all j, I j fi k. 4) CAI[k I] PA2[i] and Cl[k l] P21i] Then, increment k by 1. 5) Iterate 3 4 steps until the production of the child C1 is completed. Applying this procedure to ....

M. L. Dertouzos and A. K. Mok, "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks," IEEE Transactions on Software Engineering, vol. 15, no. 12, Dec. 1989.

....task must execute without missing its deadline or compromising other task deadlines in multiprocessor systems often becomes intractable. Besides, when the scheduling is possible, the algorithms that are optimal for uniprocessor systems are not optimal when the number of processors is increased [3] (it is well known that optimal scheduling for multiprocessors systems is NP Hard [4] Nevertheless, as a first approach it is usual to allocate periodic processes to processors and, after that, to use an optimal uniprocessor scheme on each processor individually [1] The common framework to ....

Dertouzos, M.L., Mok, A.K., "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks", IEEE Transactions on Software Engineering, v.15, n.12, pp. 1497-1506, 1989

....must execute without missing its deadline or compromising other task deadlines in multiprocessor systems often becomes intractable. Besides, when the scheduling is possible, algorithms that are optimal for uniprocessor systems are not necessarily optimal when the number of processors increases [3] (it is well known that optimal scheduling for multiprocessors systems is a NPHard problem [4] Nevertheless, the great availability of these systems has made them interesting for the real time community and the research in this area has been reactivated in the last years. Usually, two ....

.... load it is not schedulable by a global scheduler with a fixed Rate Monotonic priority (see Figure l(a) where T3 misses a deadline at time t 100) Likewise this task set is not schedulable by an Earliest Deadline First global scheduler, illustrating that EDF is not optimal for multiprocessors [3]. In contrast, using a DP global scheduler, if a promotion time equal to zero is used for task T3 then the whole system is schedulable (see Figure l(b) Additionally, there are extensions of the DP model to deal with jitters releases [19] shared resources and arbitrary deadlines [20] These ....

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Dertouzos, M.L., Mok, A.K., "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks", IEEE Transactions on Software Engineering, v.15, n.12, pp. 1497-1506, 1989

....the number c is called the competitive ratio of the on line algorithm. Furthermore, the on line algorithm is said to be 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 [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 ....

M.L. Dertouzos and A.K.L. Mok. Multiprocessor on-line scheduling of hard-realtime tasks. IEEE Transactions on Software Engineering, 15(12):1497-1506, December 1989.

....of discrete speeds and overhead. 3 Power Aware Scheduling for Independent Tasks Without precedence constraints, all tasks are available at time 0 and are ready to execute. There are two major strategies to scheduling independent tasks in multi processor systems: global and partition scheduling [10]. In global scheduling, all tasks are in a global queue and each processor selects from the queue the task with the highest priority for execution. In partition scheduling, each task is assigned to a specific processor and each processor fetches tasks for execution from its own queue. In this ....

....begins to execute. In global scheduling, the task priority assignment affects which task goes where, the workload of each processor, and the total time needed to finish the execution of all tasks. In general, the optimal solution of assigning task priority to get minimal execution time is NP hard [10]. Furthermore, we show in Section 3.3 that the priority assignment that minimizes execution time may not lead to minimal energy consumption. Expecting that longer tasks generate more dynamic slack during execution, in this paper, we use the longest task first heuristic (LTF, based on the task s ....

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M. L. Dertouzos and A. K. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Trans. On Software Engineering, 15(12):1497--1505, 1989.

....both independent and dependent tasks. 3 Power Aware Scheduling for Independent Without precedence constraints, all tasks are available at time 0 and are ready to execute. There are two major strategies to scheduling independent tasks in multi processor systems: global and partition scheduling [3]. In the global scheduling strategy, all tasks are in a global queue and each processor selects from the queue the task with the highest priority for execution. In the partition scheduling strategy, each task is assigned to a specific processor and each processor selects a task for execution from ....

....queue. In global scheduling, the priority of the tasks in the queue affects which task goes where, the workload of each processor, and the total time needed to finish the execution of all tasks. In general, the optimal solution of assigning task priority to get minimal execution time is NP hard [3]. Furthermore, we show in Section 3.3 that the priority assignment that minimizes execution time may not lead to minimal energy consumption. Expecting that longer tasks generate more dynamic slack during execution, in this paper, we use the longest task first heuristics (LTF, based on the task s ....

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M.L.Dertouzos and A.K.Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Trans. On Software Engineering, SE-15 (12): 1497-1505, 1989

....for real time applications. However, the programming of such multiprocessor systems presents a rather formidable problem. In particular, time critical tasks must be serviced within certain preassigned deadlines dictated by the physical environment in which the multiprocessor system operates [1]. Thus, efficient methods and tools for allocation and scheduling of tasks are needed. In general, a task can be characterized by an integer triple (S, C, D) where S is the start time of the task, C is the execution time of the task, and D is the deadline. A precedence relation may be defined on ....

.... [2] Henn generalized the result for a single processor case to cover precedence constraints [3] Garey and Johnson discovered optimal scheduling algorithm when there are only two processors [4] Unluckily, the scheduling problem often becomes NP hard whenever more than two processors are involved [1]. Task scheduling is simply the choice of a mapping of a set of tasks to a set of processors to achieve the pre defined objectives such as the minimization of the deadline missing time and the minimization of the communication cost. Whilst this problem requires the simultaneous optimization of ....

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M. L. Dertouzos and A. K. Mok, "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks," IEEE Transactions on Software Engineering, vol. 15, no. 12, Dec. 1989.

....to failures of external events, and it permits the dynamic activation of exception handling tasks. ffl in contrast to static scheduling, dynamic scheduling can take advantage of additional updated information regarding the system state (see section on resource reclaiming) In dynamic scheduling [2, 9], when new tasks arrive, the scheduler dynamically determines the feasibility of scheduling these new tasks without jeopardizing the guarantees that have been provided for the previously scheduled tasks. Thus for predictable executions, schedulability analysis must be done before a task s ....

....intermediate solution which tries to meet the conflicting requirements of higher schedulability and low overhead. Many practical instances of scheduling algorithms have been found to be NP complete, i.e. it is believed that there is no optimal polynomial time algorithm for them. It was shown in [2] that there does not a task is a granule of computation which is scheduled for execution exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system. These negative results motivated the need for heuristic ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989. 18

....and then highlight the limitations of these works which form the motivation for our work. 3.1 Related Work Many practical instances of scheduling problems have been found to be NP complete [2] i.e. it is believed that there is no optimal polynomial time algorithm for them. It was shown in [1] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system. These negative results motivated the need for heuristic approaches for solving the scheduling problem. Recently, many heuristic ....

M.L. Dertouzos and A.K. Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. Software Eng., vol.15, no.12, pp.1497-1506, Dec. 1989.

....is that, if a solution is found, then one can be sure that all deadlines will be met. Scheduling of aperiodic tasks whose characteristics are not known a priori requires dynamic scheduling algorithms. Complexity results show that real time multiprocessing scheduling is NP hard. It was shown in [5] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks, with or without mutual exclusion constraints, on a multiprocessor system. A heuristic search algorithm, called myopic scheduling algorithm, was proposed in [6] for tasks with resource constraints. ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

....if a solution is found, then one can be sure that all deadlines will be guaranteed. However, this approach is not applicable to aperiodic tasks whose arrival times and deadlines are not known apriori. Scheduling such tasks in a multiprocessor realtime system requires dynamic scheduling algorithms [5, 6]. In dynamic scheduling, when new tasks arrive, the scheduler dynamically determines the feasibilty of scheduling these new tasks without jeopardizing the guarantees that have been provided for the previously scheduled tasks. Thus for predictable executions, schedulability analysis must be done ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

....ratio of number of tasks feasibly scheduled to the number of tasks arrived. 3.3 Dynamic Scheduling Algorithms Many practical instances of scheduling problems have been found to be NP complete [5] i.e. it is believed that there is no optimal polynomial time algorithm for them. It was shown in [4] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system. These negative results motivated the need for heuristic approaches for solving the scheduling problem. Recently, many heuristic ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

....is that, if a solution is found, then one can be sure that all deadlines will be met. Scheduling of aperiodic tasks whose characteristics are not known a priori requires dynamic scheduling algorithms. Complexity results show that realtime multiprocessing scheduling is NP hard. It was shown in [5] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks, with or without mutual exclusion constraints, on a multiprocessor system. A heuristic search algorithm, called myopic scheduling algorithm, was proposed in [6] for tasks with resource constraints. ....

M.L.Dertouzos and A.K.Mok. Multiprocessor on-line scheduling of hard real-time tasks. IEEE Trans. on Software Engg., 15(12):14971506, December 1989.

....ratio of number of tasks feasibly scheduled to the number of tasks arrived. 3.1 Dynamic Scheduling Algorithms Many practical instances of scheduling algorithms have been found to be NP complete [4] i.e. it is believed that there is no optimal polynomial time algorithm for them. It was shown in [3] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system. These negative results motivated the need for heuristic approaches for solving the scheduling problem. For multiprocessor systems ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

.... real time systems involves scheduling of tasks within a node (local scheduling) migration of tasks to other nodes (global scheduling) if it is not possible to schedule them locally, and scheduling of messages on communication links (message scheduling) The problem of local scheduling [2,9,11] is to determine when and on which processor a given task executes. For scheduling tasks in a node, all the tasks arrive at the task scheduler (which does local scheduling) from where they are distributed to other processors in the node for execution. The task scheduler dynamically determines the ....

M.L. Dertouzos and A.K. Mok, Multiprocessor on-line scheduling of hard real-time tasks, IEEE Trans. Software Engg., 15(12) (1989), pp.1497-1506.

....is found, then one can be sure that all deadlines will be guaranteed. However, this approach is not applicable to aperiodic tasks whose characteristics are not known a priori. Scheduling such tasks in a multiprocessor real time system requires dynamic scheduling algorithms. In dynamic scheduling [3, 8], when new tasks arrive, the scheduler dynamically determines the feasibility of scheduling these new tasks without jeopardizing the guarantees that have been provided for the previously scheduled tasks. Thus for predictable executions, schedulability analysis must be done before a task s ....

....to ensure that the dispatch queues are always filled to their minimum capacity (if there are tasks left with it) for this parallel operation. This minimum capacity depends on the average time required by the scheduler to reschedule its tasks upon the arrival of a new task [10] It was shown in [3] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system. These negative results motivated the need for heuristic approaches for solving the scheduling problem. Recently, many heuristic ....

M.L. Dertouzos and A.K. Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. on Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

....later, depending on the task characteristics and in such a way as to not violate the guarantees of already scheduled tasks. 4. 1 Added Complexity of Estimation At the end of a task T j s execution on processor p i , it updates M arr[i] this takes O(1) then sets M(t) to the minimum among M arr[1] : M arr[m] this takes O(m) time) Thus the added complexity of the Estimation approach is O(m) per task finish. As Early Start and RV both run in time O(m finish, adding Estimation to them does not increase their complexity. Maintaining OldRelcaimdels[k] takes time O(1) per scheduler ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. Software Eng., vol.15, no.12, pp.1497-1506, Dec 1989.

....with the following negative results motivated the need for heuristic approaches for solving the dynamic scheduling problem. Result 1: There does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints on a multiprocessor system [20]. Result 2: For two or more processors, no deadline scheduling algorithm can be optimal without complete a prior knowledge of deadlines, computation times, and task start times [66] Many heuristic scheduling algorithms [79, 128] have been proposed to dynamically schedule a set of tasks with ....

M.L. Dertouzos and A.K. Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. Software Engg., vol.15, no.12, pp.1497-1506, Dec. 1989.

....level for each task, satisfying the timing constraints, such that the performance index of the system is maximized. A. Related Work and Motivation The problem of obtaining an optimal schedule for a set of real time tasks in a multiprocessor system is NP complete [10] Moreover, it was shown in [11] that there does not exist an algorithm for optimally scheduling dynamically arriving tasks with or without mutual exclusion constraints. These negative results motivated the need for heuristic approaches for solving scheduling problems. Various heuristics algorithms, such as Myopic scheduling [2] ....

M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks", IEEE Software Engg., vol. 15, no. 12, pp. 1497-1506, Dec. 1989.

....frequently considered. For those objective functions mostly list scheduling algorithms are adapted, e.g. Shortest Deadline First (SDF) 5] 7] Scheduling with deadline constraints is also considered for real time systems. But these systems often have periodic tasks with precedence constraints[6][8]. Results for scheduling in specific application areas are most frequently found in the areas of operating systems (e.g. 16] 14] and production systems (e.g. 5] Those application specific algorithms are not applicable for our scheduling problem in a distributed message converter system as ....

MICHAEL L.DERTOUZOS; ALOYSIUS MOK. MULTIPROCESSOR ON-LINE SCHEDULING OF HARD REAL-TIME SYSTEMS. IEEE TRANSACTIONS ON SOFTWARE ENGINEERING, 15(12), DECEMBER 1989.

....T = gcd(D 1 ; D 2 ; Dm ) If the utilization factor (U) of a set of periodic tasks is at most n (T Gamma R 1) T , a feasible schedule exists. If R 1, then the sufficient condition becomes U n. Thus this paper solves the open problem stated as a conjecture in Dertouzos and Mok s paper[1] that the condition U n is both necessary and sufficient for feasible scheduling. 1 Introduction The increasing availability of multiprocessor computer systems makes it possible to execute many tasks in parallel and thus reduce or eliminate violations of task deadlines in a variety of complex, ....

....and sufficient for feasible scheduling. 1 Introduction The increasing availability of multiprocessor computer systems makes it possible to execute many tasks in parallel and thus reduce or eliminate violations of task deadlines in a variety of complex, real time applications. Dertouzos and Mok [1] states: If a schedule exists which meets the deadlines of a set of tasks whose start times are the same, then the same set of tasks can be scheduled at run time even if their start times are different and not known a priori. In our paper, we solve the open problem stated as a conjecture in [1] ....

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M. L. Dertouzos and A. K. Mok, "Multiprocessor on-line scheduling of hard-real-time tasks," IEEE Trans. Software Eng., vol. 15, no. 12, pp. 14971506, Dec. 1989.

....systems has received signi cant attention, however, few techniques have addressed the problem of guaranteeing inter task temporal dependencies such as relative timing constraints. Most real time scheduling techniques consider the scheduling of real time tasks with ready times and deadlines [10, 11, 12, 13, 14, 15, 16, 17]. These constraints impose constant intervals in which a task must be executed. In contrast, in the presence of relative time constraints, the time window within which a task must execute may depend on the scheduling and execution parameters of the other tasks in the system. Some of the systems ....

M. L. Dertouzos and A. K. Mok. Multiprocessor On-Line Scheduling of Hard Real-Time Tasks. IEEE Transactions on Software Engineering, 15(12):1497-1506, 1989.

....scenarios, though the assumption of such extreme conditions is likely to result in under utilisation of resources. It is when dealing with uncertainties that the limitations of deterministic analysis become apparent. In assessing the e#ect of uncertainties, deterministic schedulability studies [5] are forced to take extreme positions by assuming, on the one hand, complete lack of knowledge about certain selected task attributes (such as computation time Nimal Nissanke and Amare Leulseged are with South Bank University, School of Computing, Information Systems and Mathematics, 103 Borough ....

....Systems and Mathematics, 103 Borough Road, London SE1 0AA, UK emails: nissanke sbu.ac.uk, leulseam sbu.ac.uk or deadline) and, on the other, full knowledge about other remaining attributes. The kind of conclusions that such a deterministic analysis can draw is also limited. Referring to [5] again, these concern, for example, whether or not a set of task is schedulable in an absolute sense in the absence of knowledge on a task attribute. Both positions, the assumption of the complete lack of knowledge or the full knowledge, are generally unrealistic in nature because in real life the ....

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M. L. Dertouzos and A.K. Mok. Multi-processor on-line scheduling of hard real-time systems. IEEE Trans. on Software Engineering, 15(12), December 1989.

....ratio is fixed. We adapt the lower bound for the case where the on line algorithm has faster machines than the off line algorithm. This results in a lower bound of Omega (n 1=2m 2 ) on the speed of on line machines, if = 1. We also consider the following scheduling problem studied in [3, 9]. Each job J has a deadline d(J) Instead of minimizing the flow time, we require that each job is finished by its deadline, effectively limiting the flow time of job J to d(J) Gamma r(J) The goal is to complete all jobs on time. For this problem, we give lower bounds on the speed and the ....

M. L. Dertouzos and A. K.-L. Mok. Multiprocessor on-line scheduling of hard-realtime tasks. IEEE Transactions on Software Engineering, 15:1497--1506, 1989.

....7.1. Future Work Effective uniprocessor scheduling is crucial for multimedia applications, but multiprocessor scheduling support for multimedia applications is becoming increasingly important. While some previous work has attempted to address the problem of real time multiprocessor scheduling [14][19] 21] little work has been done to address the problem of how to allow both real time and conventional applications to share resources and co exist together in a multiprocessor environment. Scheduling multimedia applications on multiprocessors poses challenges that do not arise in scheduling ....

M. Dertouzos and A. Mok, "Multiprocessor On-line Scheduling of Hard-Real-Time Tasks", IEEE Transactions on Software Engineering, 15(12), pp. 1497-1506, Dec. 1989.

....2. Algorithms with Resource Augmentation 3 bound for the case where the on line algorithm has faster machines than the o# line algorithm. This results in a lower bound of ## n 1 2m 2 ) on the speed of on line machines, if l = 1. We also consider the following scheduling problem studied in [3, 10]. Each job J has a deadline d(J ) Instead of minimizing the flow time, we require that each job is finished by its deadline, e#ectively limiting the flow time of job J to d(J) r(J) The goal is to complete all jobs on time. For this problem, we give lower bounds on the speed and the number of ....

M. L. Dertouzos and A. K.-L. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497--1506, 1989.

....for scheduling periodic tasks in a monoprocessor environment when preemption is allowed. Their results were extended to handle deadlines [14] and precedence constraints [16] Chung [12] and Dean [13] extended these results to allow the scheduling of tasks with imprecise results. Mok and Dertouzos [27] extended further these results to a multiprocessor environment. Sprunt [32] and Chetto [11] dealt with handling non periodical tasks requests over a set of periodic tasks already scheduled. Non preemptive scheduling is treated by [19] Resource constraints are handled by [15] 37] Concerning ....

Michael L.Dertouzos; Aloysius Mok. Multiprocessor On-line Scheduling of Hard Real-Time Systems. IEEE Transactions on Software Engineering, 15(12), December 1989.

.... k server and generic task system problems [23, 21, 5] While the single request sequence model captures many important problems, there are many others which do not fall into this category, such as some operating system scheduling problems [18, 12, 13, 24] and some real time scheduling problems [20, 4, 11]. In a typical problem, there is a single system resource such as a processor and, at any given time, there are multiple requests in the system waiting to be serviced. As a result, the underlying problem is deciding which current request should the system service rather than which system resource ....

M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497-1506, 1989.

....viewpoint, EDF except in some simple settings has no performance guarantee, i.e. its performance cannot match or even be competitive against the o line adversary. It is indeed known that in many settings of deadline scheduling, no online algorithm has this sort of performance guarantee [1, 5]. In recent years, a plausible approach to studying performance guarantee is to allow the online scheduler to use faster processors than the o line adversary [2, 6, 7, 10, 12] Intuitively, using faster processors compensate the online scheduler for the lack of future information In particular, ....

M. L. Dertouzos and A. K. L. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15(12):14971506, 1989.

....[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 preempted in. Koren and Shasha [9] give an algorithm (MOCA) with a competitive guarantee for a multiprocessor ....

M. L. Dertouzos and A. K-L. Mok. Multiprocessor on-line scheduling of hard real-time tasks. IEEE Trans. on Software Engineering, 15(12):1497--1506, 1989.

....can be synthesized to implement low overhead optimistic synchronization. 1 Introduction The scheduling of independent real time tasks is well understood, as optimal scheduling algorithms have been proposed for periodic and aperiodic tasks on uniprocessor [7, 9] and multiprocessor systems [8, 4, 15]. However, if the tasks communicate through shared critical sections, a low priority task that holds a lock may block a high priority that requires the lock, causing a priority inversion. In this paper, we present a method for real time synchronization that avoids priority inversions. Rajkumar, ....

A.K. Mok and M.L. Dertouzos. Multiprocessor on-line scheduling of hard real-time tasks. IEEE Trans. on Computers, 15(12):1497--1506, 1989.

....problems have de ed all previous (worst case) analytic attempts to identify e ective on line algorithms for solving them. For example, Dertouzos and Mok proved that no on line algorithm can legally schedule all feasible input instances of the hard real time scheduling problem for m 2 machines [7]. Furthermore, there is no obvious notion of an approximation algorithm 1 for this problem since all jobs must be completed. For the various versions of the ow time problem, while approximations are acceptable, a variety of results ( 20, 24] summarized in Section 1.3.2) show that no on line ....

.... no (1 ) speed algorithms exist for either problem for small (1=5 for meeting deadlines and 1=21 for ow time) More speci cally, for preemptive hard real time scheduling, we analyze two simple and widely used on line algorithms, earliest deadline rst (EDF) 6] and least laxity rst (LLF) [7]. At time t in an m processor system, EDF schedules the m jobs currently in the system which have the earliest deadlines while LLF schedules the m jobs currently in the system which have the smallest laxities (at time t, a job J j has laxity (d j t) p j x j ) where x j is the amount of processing ....

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M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497-1506, 1989.

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M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497--1506, 1989.

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M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497--1506, 1989.

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Dertouzos, M. and A.K. Mok (1989). Multiprocessor on-line scheduling of hard real-time tasks.

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M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497-1506, 1989.

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M. Dertouzos and A. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15:1497-1506, 1989.

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Dertouzos, M.L., Mok, A.K.L.: Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering 15 (1989) 1497--1506

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M. L. Dertouzos and A. K. Mok, "Multiprocessor on-line scheduling of hard-real-time tasks," IEEE Transactions on Software Engineering, vol. 15, no. 12 (December 1989), pp. 1497-1506.

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Dertouzos, M.L., Mok, A.K., "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks", IEEE Transactions on Software Engineering, v.15, n.12, pp. 1497-1506, 1989

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M. L. Dertouzos and A. K. Mok, "Multiprocessor on-line scheduling of hard-real-time tasks," IEEE Transactions on Software Engineering, vol. 15, no. 12 (December 1989), pp. 1497-1506.

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M.L. Dertouzos and AK-L. Mok, "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks," IEEE Trans. Software Eng., Dec. 1989, pp. 14971506.

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M. L. Dertouzos and A. K. L. Mok. Multiprocessor On-Line Scheduling of Hard-RealTime Tasks IEEE Transactions on Software Engineering, 15(12): 1497--1506, 1989.

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M. L. Dertouzos and A. K. Mok, "Multiprocessor on-line scheduling of hard-real-time tasks," IEEE Transactions on Software Engineering, vol. 15, no. 12 (December 1989), pp. 1497-1506.

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M. L. Dertouzos and A. K. L. Mok. Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks IEEE Transactions on Software Engineering, 15(12): 1497--1506, 1989.

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M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. Software Eng., vol.15, no.12, pp.1497-1506, Dec 1989.

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M.L. Dertouzos and A.K.-L. Mok, "Multiprocessor On-Line Scheduling of Hard-Real-Time Tasks," IEEE Trans. Software Eng., vol. 15, no. 12, pp. 1497-1506, Dec. 1989.

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M. L. Dertouzos and A. K. Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Trans. On Software Engineering, 15(12):1497--1505, 1989.

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M.L.Dertouzos and A.K.Mok, "Multiprocessor on-line scheduling of hard real-time tasks," IEEE Trans. Software Eng., vol.15, no.12, pp.1497-1506, Dec 1989. 14

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M.L.Dertouzos and A.K.Mok "Multiprocessor On-Line Scheduling of Hard-Real Time Tasks". IEEE transactions on Software Engineering. December, 1989.

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