S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, February 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of real time tasks on a single processor can be readily adapted to accommodate more practical needs of real time systems, such as, the scheduling of soft deadline tasks [10] the scheduling of tasks which need to be synchronized [20] and the mode change protocols [19] 23] Dhall and Liu [5] were the first to propose heuristic algorithms to solve this problem. They proposed two scheduling algorithms, which were called the Rate Monotonic Next Fit (RMNF) and Rate Monotonic First Fit (RMFF) and analyzed their performance. The worst case performance of RMNF and RMFF was proven to have a ....

....tasks to be scheduled. This condition is a worst case condition, and therefore it is referred to as Condition WC (Worst Case) The function f (m) is a strictly decreasing function with regards to m, the number of tasks on a processor. In studying the performance of RMNF and RMFF, Dhall and Liu [5] used a different schedulability condition, which is stated as follows: Condition IP: Let be a set of tasks with periods . Let . If C m T m 2(1 u (m 1) m1) 1, then the set can be feasibly scheduled by the rate monotonic scheduling algorithm. As m approaches infinity, the minimum ....

[Article contains additional citation context not shown here]

S.K. DHALL AND C.L. LIU, "On a Real-Time Scheduling Problem," Operations Research 26, 127-140 (1978).

....for execution the highest priority tasks from this queue. Unfortunately, using this approach with optimal uniprocessor scheduling algorithms, such as the rate monotonic (RM) and earliest deadline first (EDF) algorithms, may result in arbitrarily low processor utilization in multiprocessor systems [11]. However, recent research on proportionate fair (Pfair) scheduling has shown considerable promise in that it has produced the only known optimal method for scheduling periodic tasks on multiprocessors [1, 3, 5, 19, 24] In partitioning, each task is assigned to a single processor, on which each ....

....and migration constraints are on the y axis. In general, increasing distance from the origin may imply greater generality. Of these nine classes, 1, 1) 2, 1) and (3, 3) restricted algorithms have received the most attention. For example, 1, 1) restricted algorithms have been studied in [7, 11, 21, 22], while (2, 1) restricted algorithms (and equivalently, 3, 1) restricted algorithms) have been studied in [8, 9, 11] The class of (3, 3) restricted algorithms has been studied in [1, 5, 16, 24] In addition to these, 1, 3) and (2, 3) restricted algorithms were recently considered in [4] and ....

[Article contains additional citation context not shown here]

S. Dhall and C. Liu. On a real-time scheduling problem. Operations Research, 26:127--140, 1978. 28

....[26] Producing a competitive global scheduler, based on such well understood uniprocessor algorithms, has proved to be a daunting task. In fact, Dhall and Liu have shown that global scheduling using either EDF or RM can result in arbitrarily low processor utilization in multiprocessor systems [13]. Partitioning, regardless of the scheduling algorithm used, has two primary flaws. First, it is inherently suboptimal when scheduling periodic tasks. A well known example of this is a two processor system that contains three synchronous periodic tasks, each with an execution cost of 2 and ....

....many other available partitioning heuristics will likely be impractical for online scheduling. Despite this, partitioning is beneficial in that, once tasks are assigned to processors, each processor can be scheduled independently using uniprocessor scheduling algorithms such as RM and EDF [8, 13, 27, 31, 36]. One of the most popular approaches is RM FF, in which the FF heuristic is used to assign tasks to processors, which are scheduled using the RM algorithm. The popularity of this approach stems largely from the popularity of RM as a uniprocessor scheduling algorithm. One reason for RM s popularity ....

S. Dhall and C. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, 1978.

....of each task meets its deadline. The timing behavior of a RTES depends on the task allocation scheme, scheduling scheme and scheduling algorithm. In our following discussion, we assume static task allocation, preemptive scheme and rate monotonic (RM) algorithm due to their respective advantages [2,3,8,9,11] and wide usage. Given the above, one approach to predict feasibility is to simulate the system execution for a given schedule. However, the simulation approach can be computationally expensive [7] It has been shown that predicting the timing performance of a general task system is an NP complete ....

....(a i ) and computation time (c ) for each task (t i ) The ranges for period and computation time were chosen so as to obtain a reasonably good number of fairly uniformly distributed values for the various metrics to be introduced in the next section. In our study the ranges were [10,8500] and [2,950] respectively. Another limitation on the upper limit of periods is the fact that having a higher value would lead to unnecessarily long validation time. Clearly, the deadline for any meaningful system should be greater than their corresponding sum of computation time and activation. Also, since we ....

S. K. Dhall, and C. L. Liu, "On a real-time scheduling problem ", Operations Research, Vol. 26, No. 1, January, 1978, pp. 127-140.

.... multiprocessor platform (where EDF denotes the Earliest Deadline First scheduling algorithm) to our knowledge, there has been no prior work done on static priority scheduling upon uniform multiprocessors The partioned approach to static priority scheduling upon has been extensively studied [6, 3, 4, 10] for identical multiprocessors. Much of this research has adopted the approach of using bin packing like algorithms for partitioning a given set of periodic tasks among a set of processors such that each partition is uniprocessor feasible under the rate monotonic algorithm; e.g. Dhavri and Dhall ....

DHALL, S. K., AND LIU, C. L. On a real-time scheduling problem. Operations Research 26 (1978), 127--140.

....algorithm in uniprocessor systems a task set # is feasible on a uniprocessor # if and only if it is EDF schedulable on #. Unfortunately, EDF is not optimal on multiprocessors since there are tasks sets that are feasible on some multiprocessors but will miss deadlines if EDF is used [2]. There are nevertheless significant advantages to using EDF for scheduling on multiprocessor platforms. While it is beyond the scope of this paper to describe in detail these advantages, some important ones are listed below: Very e#cient implementations of EDF have been designed (see, e.g. ....

Dhall, S. K., and Liu, C. L. On a real-time scheduling problem. Operations Research 26 (1978), 127--140.

....scheduling algorithm in uniprocessor systems a task set is feasible on a uniprocessor if and only if it is EDF schedulable on . Unfortunately, EDF is not optimal on multiprocessors since there are tasks sets that are feasible on some multiprocessors but will miss deadlines if EDF is used [1]. There are nevertheless signi cant advantages to using EDF for scheduling on multiprocessor platforms. While it is beyond the scope of this paper to describe in detail these advantages, some important ones are listed below: Very ecient implementations of EDF have been designed (see, e.g. ....

Dhall, S. K., and Liu, C. L. On a real-time scheduling problem. Operations Research 26 (1978), 127-140.

....of the algorithm. The paper concludes with Section 7. 2RELATED WORK Task assignment and scheduling problems are studied extensively in both fields of Operations Research and Computer Science [6] 7] 8] 9] 10] 11] 12] 13] 14] For a set of independent periodic tasks, Dhall and Liu [15] and their colleagues developed various assignment algorithms based on the rate monotonic scheduling algorithm [16] or intelligent fixed priority algorithm [17] However, if there exist precedence constraints among tasks like our task system, these algorithms cannot be used. Instead, an approach ....

S.K. Dhall and C.L. Liu, "On a Real-Time Scheduling Problem," Operations Research, vol. 26, no. 1, pp. 127-140, 1978.

....might be scheduled when its own queue is empty and ready aperiodic tasks are waiting in other queues. 14 In the case of hard aperiodic tasks scheduled using the EDF algorithm, it is better to partition. In the global queue case, using EDF can result in arbitrarily low utilization, as shown in [10]. The example presented there involves three tasks with (execution requirement, deadline) parameters of (2, p) 2, p) and (p, p 1) respectively, where p # 4. Note that this task set can be easily scheduled on two processors using partitioning. However, global EDF does not schedule this task ....

....time of the aperiodic tasks. From the figure, we can see that the aperiodic tasks finish at times 4, 7, 12, and 13, respectively. Note that the fourth aperiodic task is serviced only after the completion of the third aperiodic task at time 12. Also note that a processor is idle in the interval [10, 11]. Thus, the fourth aperiodic task could actually have run in parallel with the third in slot 10. One way to utilize this extra processor time is to have a set of background servers, one on each processor. Such a server is scheduled if its processor becomes idle while unfinished aperiodic tasks ....

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, 1978.

....important difference between the partitioned and global approaches. While the partitioned approach can rely on well known optimal uniprocessor priority assignment schemes, it is not clear as to what priority assignment scheme should be used for the global approach. The following example by Dhall [10] demonstrates that traditional uniprocessor priorityassignment schemes do not work well for global multiprocessor scheduling. Consider a periodic task set with task priorities assigned in inverse proportion to their periods (i.e. rate monotonic scheduling) # def = # 1 = 2#, 1) # 2 = 2#, ....

....( # 2 1) m 1) m. Among the global approaches, only RM US[m (3m 2) has a tight system utilization bound, namely the derived bound of m (3m 2) For adaptiveTkC, the bound has been shown to be no greater than 2 m 3 m 1 # 5 m 2 6m 1 [2] For RM, the bound is known to be no greater than 1 m [10]. For WM, no known utilization bound has hitherto been proven; however, due to the reasoning above the system utilization bound of WM cannot be higher than 1 2. Based on the expressions above for the system utilization bounds, we see that Algorithm RM US[m (3m 2) is inferior to the best ....

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, 1978.

.... outperforms RM when many processors are available and A is small (tasks have a low average utilization) The reason for this is that RM US[m (3m 2) always succeeds to schedule task set with a system utilization less than m (3m 2) while RM can potentially fail due to Dhall s effect [9]. As A becomes larger RM and RM US[m (3m 2) offer comparable performance since most tasks then have a utilization greater than the guarantee bound of m (3m 2) For example, when m = 32 and A 0:7, most tasks have a utilization greater than 32= 3 32 3) 0:34, which means that RM and ....

....1 2. Among the studied approaches, only RM US[m (3m 2) has a tight utilization bound, namely the derived bound of m= 3m 2) For adaptiveTkC, the utilization bound has been shown to be no greater than 2 m 3 m 1 p 5 m 2 6 m 1 [2] For RM, the utilization bound is known to be no greater 1=m [9]. For WM, no known utilization bound has hitherto been proven; however, due to the reasoning above the utilization bound cannot be higher than 1 2. We can thus conclude that, in general, no static priority scheduling algorithm on a multiprocessor can achieve a utilization bound that is greater ....

[Article contains additional citation context not shown here]

DHALL, S. K., AND LIU, C. L. On a real-time scheduling problem. Operations Research 26 (1978), 127--140. 17

No context found.

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, February 1978.

No context found.

S. K. Dhall and C. L. Liu, "On a Real-Time Scheduling Problem," in Operations Research, vol. 26(1), pp. 127--140, Feb. 1978.

No context found.

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, February 1978.

No context found.

Dhall, S. K. and Liu, C. L., "On a Real-Time Scheduling Problem," Operations Research 26(1) (February 1978) pp.127-140.

No context found.

S. K. Dhall and C. L. Liu. On a Real-Time Scheduling Problem. In Operations Research Vol. 26, pp. 127-140, 1978.

No context found.

S. K. Dhall and C. L. Liu. On a Real-Time Scheduling Problem. In Operations Research Vol. 26, pp. 127-140, 1978.

No context found.

DHALL, S. K., AND LIU, C. L. On a real-time scheduling problem. Operations Research 26 (1978), 127--140.

No context found.

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, January /February 1978.

No context found.

S.K. Dhall, C.L. Liu, \On a real-time scheduling problem", Operations Research 26 (1) (1998) 127-140.

No context found.

S. K. Dhall and C. L. Liu. On a Real-Time Scheduling Problem. In Operations Research Vol. 26, pp. 127-140, 1978.

No context found.

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, January /February 1978.

No context found.

S.K. DHALL AND C.L. LIU, "On a Real-Time Scheduling Problem," Operations Research 26, 127-140 (1978).

No context found.

S. K. Dhall and C. L. Liu. On a real-time scheduling problem. Operations Research, 26(1):127--140, January /February 1978.

No context found.

DIdALL, S.K.. and LIU, C.L.: 'On a real-time scheduling problem', Oper. Res., 1978, :6, (1), pp. 127-140

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC