Overview of Scheduling a Mix of Periodic and Aperiodic Tasks

Transcription

1 Overview of Scheduling a Mix of Periodic and Aperiodic Tasks Minsoo Ryu Department of Computer Science and Engineering

2 2 Naive approach Background scheduling Algorithms Under static priority policy (RM) Polling Server Deferrable Server Priority Exchange Sporadic Server Slack Stealing Under dynamic priority policy (EDF) Dynamic Priority Exchange Total Bandwidth Server Constant Bandwidth Server 2

3 3 Background Scheduling Aperiodic tasks are executed when there is no periodic task (period, execution time) to execute task 1 (6, 2) and task 2 (10, 4) 3

4 4 Polling Server A periodic task is created (period =, capacity = C ) T0 0 It is assigned a priority according to the rate monotonic algorithm It is subject to preemption by higher priority tasks Scheduling of PS (polling server) PS is ready and its capacity is replenished at the start of its period PS services aperiodic task arrivals until either it exhausts its execution time C 0 or there is no aperiodic work left to be executed In the latter case, PS loses any of unused execution time and is unable to service aperiodic tasks until the start of its next period 4

5 5 Polling Server Example Polling Server (5, 2), task 1 = (4, 1), and task 2 = (6, 2) 5

6 6 Deferrable Server A periodic task is created (period =, capacity = C ) T0 0 In general, it is assigned a priority according to the rate monotonic algorithm In practice, we often consider it at the highest priority level Scheduling of DS (deferrable server) DS is ready and its capacity is replenished at the start of its period DS services aperiodic task arrivals until it exhausts its execution time C 0, or until the end of its period is reached Unlike PS, DS does not lose its unused execution time and is able to service aperiodic tasks throughout its entire period DS loses any of its unused execution time at the end of its period 6

7 7 Deferrable Server Example Deferrable Server (5, 2), task 1 = (4, 1), and task 2 = (6, 2) 7

8 8 Deferrable Server Schedulability condition for periodic tasks with DS The DS task violates one of Liu and Layland assumptions, namely that the task is ready at the start of the task period The DS task can defer its execution time until later in its period Critical instant (worst case phasing) Simultaneous arrivals of periodic task 0 T0 2T0 3T 0 4T0 5T0 8

9 9 Deferrable Server Time demand analysis for periodic tasks only i t t Ci Ii, t :1 i n : 1 t t I t i i j 1 1 t T j C j Total time demand with DS C 0 C 0 t T T0 0 i j 1 t T j C j Simultaneous arrivals of periodic task 0 T0 2T0 3T 0 4T0 5T0 9

10 10 Priority Exchange A periodic server is created (period = T, capacity = C) Scheduling If there are no aperiodic tasks, the server exchanges its priority with a lower priority periodic task allowing the periodic task to run The server s capacity is not lost, but preserved at a low priority Replenishment The computation time allowance for the server is replenished at the start of its period 10

11 11 Priority Exchange Example Server (5, 1) task 1 = (10, 4) task 2 = (20, 8) 11

12 12 Sporadic Server Sporadic server retains the advantages of DS and PE algorithms Scheduling The server preserves its server execution time at its priority level until an aperiodic request occurs If there are enough aperiodic tasks in an invocation, it serves up to the server s capacity Replenishment The computation time allowance for the server is replenished after some or all of the execution time is consumed by aperiodic task execution Sporadic server can be treated as a standard periodic task 12

13 13 Sporadic Server Example 13

14 14 Sporadic Server Example 14

15 15 Slack Stealing Slack stealing No periodic server Steals time from periodic tasks without causing any deadline misses Slack = deadline current time execution time Slack stealer Relies on the exact schedulability conditions for RM and DM Find the slack available by mapping out the processor schedule for the hard periodic tasks over their hyperperiod The slack values are stored in a table (off-line computation) Is optimal in the sense that it minimizes the response time of soft aperiodic tasks 15

16 16 Slack Stealing Example Without aperiodics Aperiodics (execution time) A1 A2 A (arrival time) Aperiodics A1 A3 A3 after periodics A1 A Slack stealing scheduling A1 A 1 A A3 A3 16

17 17 Total Bandwidth Server Used under EDF policy Algorithm When the kth aperiodic request arrives at time t = r k It receives a deadline d k = max(r k, d k-1 ) + C k /U s C k is the execution time of the request U s is the server s utilization factor The request is scheduled as any other standard periodic request Schedulability condition U p + U s <= 1 U p : utilization of periodic tasks 17

18 18 Total Bandwidth Server Example 18

19 19 Constant Bandwidth Server Used under EDF policy Algorithm A. Characterized by a budget c s, deadline d s,k, and (Q s, T s ) Q s : maximum budget, T s : server period, U s : Q s /T s Initially, c s = Q s and d s,0 = 0 B. Each soft job J i is assigned a dynamic deadline equal to d s,k Scheduled with dynamic d s,k under EDF consuming the server budget C. When c s = 0, the server budget is recharged to the maximum Q s and a new server deadline is generated as d s,k+1 = d s,k + T s The new server deadline means that soft jobs have dynamic deadlines D. When a new job J i arrives at r i and the server is idle (no pending job), if c s >= (d s,k r i )U s, then the server generates a new deadline as d s,k+1 = r i + T s and the server budget is recharged to the maximum Q s 19

20 20 Constant Bandwidth Server Example Task 1: execution time = 2, period = 3 CBS: max budget = 2, period = 7 20