Chen, Yingming

Lu, Chenyang

English

Washington University St. Louis: Open Scholarship

Washington University in St. Louis Washington University Open Scholarship All Computer Science and Engineering Research Computer Science and Engineering Report Number: WUCSE-2006-55 2006-01-01 Flexible Maximum Urgency First Scheduling for Distributed Real-Time Systems Yingming Chen and Chenyang Lu Follow this and additional works at: https://openscholarship.wustl.edu/cse_research  Part of the Computer Engineering Commons, and the Computer Sciences Commons Recommended Citation Chen, Yingming and Lu, Chenyang, "Flexible Maximum Urgency First Scheduling for Distributed Real-Time Systems" Report Number: WUCSE-2006-55 (2006). All Computer Science and Engineering Research. https://openscholarship.wustl.edu/cse_research/206 Department of Computer Science & Engineering - Washington University in St. Louis Campus Box 1045 - St. Louis, MO - 63130 - ph: (314) 935-6160. Department of Computer Science & Engineering2006-55Flexible Maximum Urgency First Scheduling for Distributed Real-TimeSystemsAuthors: Yingming Chen, Chenyang LuType of Report: OtherDepartment of Computer Science & Engineering - Washington University in St. LouisCampus Box 1045 - St. Louis, MO - 63130 - ph: (314) 935-61602 Flexible Maximum Urgency First SchedulingIn the rest of this report, we first describe the design of the FMUF schedulingstrategy. Then, we present simulation results to demonstrate that FMUF canprovide performance isolation for mission-critical tasks.2 FMUF SchedulingThe following are some definitions for FMUF Scheduling strategy:-Two types of tasks: mission-critical tasks and best effort tasks,categorizedby its importance specified by users.-All real-time priorities are divided into two classes: a high priority classand a low priority class. A task whose priority is in the high priority class isin the high group. The other tasks are in the low group. That is, a task in thehigh group always has a higher priority than any tasks in the low group. Insideeach group, all tasks are ordered by their end-to-end deadline, and end-to-endDeadline Monotonic scheduling algorithm is applied to assign subpriorities.The basic idea of FMUF is to utilize an adaptive mechanism to dynamicallyadjust the priority of best effort tasks (i.e., move some best effort tasks into orout of the high group) according to the current conditions at runtime. In therest of this section, we present two approaches to implement this strategy.2.1 End-to-end Task ModelA system has m end-to-end periodic tasks {Ti|1 ≤ i ≤ m} executing on nprocessors {Pi|1 ≤ i ≤ n}. Task Ti is composed of a chain of subtasks {Tij |1 ≤j ≤ ni} that may be allocated to multiple processors.A subtask Tij(1 ≤ j ≤ ni)cannot be released for execution until its predecessor Ti,j−1 is completed. a non-greedy synchronization protocol (e.g., release guard [1]) is used to enforce theprecedence constraints between subsequent subtasks.Hence, each subtask Tij ofa periodic task Ti is also periodic and shares the same rate as Ti. Each task Tiis subject to an end-to-end relative deadline related to its period.2.2 FMUF based on deadline miss ratioIn this approach the priorities of some best effort tasks are adjusted based onthe history of deadline miss. We first introduce several notations:– T0: the best effort task whose priority has just been adjusted in the latestadaptation operation– Ui,k: the total utilization of processor )Pi during the kth sampling period– Si: the set of processors that host subtasks of TiThe Logic of FMUF1. At the start time of the system, place all mission-critical tasks into the highgroup(by assigning high priority to them); and add all best effort tasks intothe low group(by assigning low priority to them); set T0 = nullFlexible Maximum Urgency First Scheduling 32. In the end of every sampling period, monitor the total utilizations {Ui,k|1 ≤i ≤ n} of all processors and check the deadline miss of all tasks(a) If there is deadline miss in the high group, move a best effort task Tsfrom the high group to the low group(by decreasing its priority), and setT0 = Ts(b) If (i) there is no deadline miss in the high group for consecutive N(N > 1) sampling periods and (ii) there are deadline misses in the lowgroup, choose one best effort task Ts from the low group according tosome selection policies(e.g., shortest end-to-end deadline first)i. If Ts 6= T0, then move Ts to the high group (by increasing itspriority), and set T0 = Tsii. Else calculate∆Ui = Ui,k−1−Ui,k for all processors in Ss; if minPi∈Ss∆Ui ≥threshold, then move Ts to the high groupIn this appraoch, an adaptation operation can be triggered by several rea-sons, such as the arrival and departure of mission-critical tasks, and significantvariation of execution times. The threshold is defined to avoid oscillation of thesystem, i.e., one task has been moved into and out of the high group repeatedly.The value of threshold need to be tuned.Here is one simple example to demonstrate how FMUF works. In this ex-ample, we set N = 5 and threshold = 5%. The workload includes 7 tasks:three mission-critical tasks, T1 with end-to-end deadline D1 = 400, T2 withD2 = 500, and T3 with D3 = 600; four best effort tasks, T4 with D4 = 350,T5 with D5 = 300, T6 with D6 = 400, and T7 with D7 = 550. There are twoprocessors. Each task has one subtask on each processor. In the beginning ofthe (k − 1)th sampling period, there is no deadline miss for all tasks. All threemission-critical tasks are in the high group, whereas there are two best efforttasks, T4 and T5, in the high group. Other two best effort tasks are in the lowgroup. During the (k− 1)th sampling period, execution time of T1 increases sig-nificantly, which incurs T3 miss deadline. An adaptation operation is triggeredat the end of (k − 1)th sampling period. The best effort task with the longestend-to-end deadline in the high group,T4 here, is moved to the low group. T0 isset to T4. For the next 10 sampling periods, there is no deadline miss in the highgroup while deadline miss occurs in the low group. Adaption operation is trig-gered in the end of each sampling period. However, as Ts is always equal to T0and the utilization deviations of two processors are both less than the threshold5%, no task will be moved to the high group according to the algorithm. At theend of (k + 10)th sampling period, T2 departs from the system. The utilizationof either T21 or T22 is greater than 5%. Then after the adaption operation, T4will be moved back to the high group. In this example, we select the best efforttask to adjust priority according to the end-to-end deadline in order to decreasethe priority inversion. We can easily replace this with other selection policies.2.3 FMUF based on AUB conditionIn this algorithm, we try to adjust the priority of some best effort tasks basedon Aperiodic Utilization Bound(AUB) for end-to-end tasks [2]. We use AUB4 Flexible Maximum Urgency First Schedulingto guarantee all tasks in high group meet their deadlines. The schedulabilitycondition of Aperiodic Utilization Bound is computed by:N∑j=1Uj(1− Uj/2)1− Uj ≤ 1 (1)N is the number of processors;Uj is the estimated utilization of subtasks in highgroup on processor j, Uj =∑Ti∈Gj Cij/Di. For simplicity, in the rest of thissection, we call inequation 1 AUB Condition.Before we describe the logic of the algorithm ,we first introduce two notations:– Bh: set of best effort tasks in the high group– Bl: set of best effort tasks in the low groupThe Logic of FMUF1. At the start time of the system, place all mission-critical tasks into the highgroup(by assigning high priority to them), and add all best effort tasks intothe low group(by assigning low priority to them);2. in the end of every sampling period, check the AUB condition(a) If AUB condition is satisfied: select one task T from Bl and check thenew AUB condition for the high group after including T ; if new AUBcondition is not violated, move T into the high group; select another taskfrom Bl and repeat this test until all tasks in Bl have been tested(b) Else AUB condition is violated: move one task T ′ from Bh to the lowgroup and check the new AUB condition for the high group after ex-cluding T ′; if new AUB condition is not satisfied yet, select another taskfrom Bh and repeat this process until the new AUB condition is satisfiedor Bh is empty3 Simulation ResultsIn this section, we evaluate the performance of the first approach presented intSection 2.2. The simulation runs on the EUCON simulator with a medium-sizedworkload that comprises of 11 end-to-end tasks. The task set includes 4 mission-critical tasks and 7 best-effort ones. Each task has 6 subtasks, which are deployedon 6 different processors(for simplicity, subtask i on processor i, 1 ≤ i ≤ 6 ). Theworkload parameters are shown in Table 1. ET1-ET6 are corresponding to theexecution times of subtask1-subtask6. There are only 6 different execution times:35,40,55,65,70, and 90. Criticality = 1 means miss-critical task; criticality = 0is corresponding to best-effort task. The time unit of execution time and periodis millisecond. We assume each task’s end-to-end deadline is equal to its period.In the beginning, only first 10 tasks run. Task 11 will arrive later. The controlperiod Ts = 100s. Other two parameters for FMUF are chosen like this: N = 5,threshold = 5%.Flexible Maximum Urgency First Scheduling 500.050.10.150.20.250.30.350.40.450.50 2000 4000 6000 8000 10000Thousandstime (ms)miss ratiomiss ratio of critical tasks miss ratio of best effort tasks(a) FMUF:deadline miss0246810120 2000 4000 6000 8000 10000Thousandstime (ms)task number in high group(b) FMUF:task number in high group00.10.20.30.40.50.60.70.80.90 2000 4000 6000 8000 10000Thousandstime (ms)utilization(c) FMUF:utilization of P100.050.10.150.20.250.30.350.40.450.50 2000 4000 6000 8000 10000Thousandstime (ms)miss ratiomiss ratio of critical tasks miss ratio of best effort tasks(d) MUF:deadline miss00.050.10.150.20.250.30.350.40.450.50 2000 4000 6000 8000 10000Thousandstime (ms)miss ratiomiss ratio of critical tasks miss ratio of best effort tasks(e) DMS:deadline missFig. 1. Experimental results: FMUF, MUF, and DMSIn the experiment, the system runs for 10000 seconds. We create three sce-narios to evaluation the performance of FMUF: 1) at 2500 seconds, executiontimes of all subtasks are decreased by 10%; 2) at 5000 seconds, task 11 arrives; 3)at 7500 seconds, execution times of all subtasks are increased by 10%. In orderto evaluate the performance of FMUF, we compare it with two baselines: MUFand DMS. We plot the results in Figure 1. The FMUF control operation is trig-6 Flexible Maximum Urgency First SchedulingTable 1. workload parameters(ms)Tasks ET1 ET2 ET3 ET4 ET5 ET6 period criticality1 55 40 65 55 40 65 700 12 90 65 70 90 65 70 1000 13 65 70 65 70 55 65 900 14 35 40 40 35 35 40 500 05 70 65 65 55 65 70 800 06 70 65 90 70 90 70 1200 07 40 55 35 40 40 35 600 08 65 55 55 70 40 55 700 09 70 65 65 90 70 65 900 010 35 40 35 35 40 35 400 011 65 55 65 70 65 70 700 1gered four times: in the initial stage, three best-effort tasks are moved into highgroup; after scenario 1, two more best-effort tasks are moved into high group;after scenario 2, two best-effort tasks are move back to low group; after scenario3, another two best-effort tasks are degraded into low group.The results showsthat FMUF can provide performance isolation for mission-critical tasks.References1. Jun Sun, Jane W.-S. Liu, I.: Synchronization Protocols in Distributed Real-TimeSystems. ICDCS(1996)2. Tarek F. Abdelzaher, Gautam H. Thaker, Patrick J. Lardieri, I.: A Feasible Regionfor Meeting Aperiodic End-to-End Deadlines in Resource Pipelines. ICDCS (2004)436-445

Flexible Maximum Urgency First Scheduling for Distributed Real-Time Systems

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Flexible Maximum Urgency First Scheduling for Distributed Real-Time Systems

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