ure Outline edulability tests for fixed-priority systems ctical factors nues from material in lecturee 5, with the same assumption

Transcription

1 riority-driven Scheduling f Periodic Ta asks (2) Embedded Softw ware Lectu ure 6 Real-Time

2 ure Outline edulability tests for fixed-priority systems onditions for optimality and schedulability eneral schedulability tests and time demand analysis ctical factors on-preemptable regions elf-suspension ontext switches imited priority levels nues from material in lecturee 5, with the same assumption

3 mality and Schedulability will recall: DF and LST dynamic priority scheduling optimal: Always produce a feasible schedule if one exists on a single processor, as long a preemption is allowed and jobs do not contend for resources Lecture 3 + confirmation last lecture: U EDF = 1 ixed priority algorithms is non-optimal in general: e.g. RM and DM sometimes fail to schedule tasks that can be scheduled using oth algorithms Proof: ence introduced schedulability testss in lecture 5

4 mality of RM and DM Algorithms ed priority algorithms can be optimal in restricted systems mple: M and DM are optimal in simply periodic systems system of periodic tasks is simply periodic if the period of each task is an ultiple of the period of the other tasks: p k = n p i where p i < p k and n is a positive integer; for all T i and T k rue for many real-world systems, e.g. the helicopter flight control system iscussed in lecture 1

5 mality of RM and DM Algorithms orem: A system of simply periodic, independent, preempt s with D i p i is schedulable on one processor using the R rithm if and only if U 1 orollary: The same is true for the DM algorithm of: simply periodic system, assume tasks in phase Worst case execution time occurs when tasks in phase i misses deadline at time t where t is an integer multiple of p i Again, worst case D i = p i imply periodic t integer multiple of periods of all higher priority tasks otal time required to complete jobs with deadline t is nly fails when U i > 1

6 dulability of Fixed-Priority Tasks ntified several simple schedulability tests for fixed-priority eduling: system of n independent preemptable periodic tasks with D i = p i c easibly scheduled on one processor using RM if U system of simply periodic independent preemptable tasks with D i chedulable on one processor using the RM algorithm iff U 1 similar results for DM] : there are algorithms and regions of operation where we d e a schedulability test and must resort to exhaustive simul s there a more general schedulability test? es, extend the approach taken for simply periodic system schedula

7 d-priority Tasks: Schedulability Test ed priority algorithms are predictable and do not suffer fro eduling anomalies he worst case execution time of the system occurs with the worst case exec ime of the jobs, unlike dynamic priority algorithms which can exhibit anom ehavior this as the basis for a general schedulability test: ind the critical instant when the system is most loaded, and has its worst esponse time se time demand analysis to determine if the system is schedulable at that nstant rove that, if a fixed-priority system is schedulable at the critical instant, it lways schedulable

8 ing the Critical Instant itical instant for a job is the worst-case release time for th, taking into account all jobs that have higher priority.e. a job released at the same instant as all jobs with higher priority eleased, and must wait for all those jobs to complete before it execu he response time of a job in T i released at a critical instant is called aximum (possible) response time, and is denoted by W i schedulability test involves checking each task in turn, to ify that it can be scheduled when started at a critical instan f schedulable at all critical instants, will work at other times ore work than the test for maximum schedulable utilization, but le han an exhaustive simulation

9 ing the Critical Instant itical instant of a task T i is a time instant such that: f w i,k D i,k for every J i,k in T i, then he job released at that instant has the maximum response time of a n T i and W i = w i,k. All jobs meet deadlines, but this instant is when the job with the slowes response is started lse if there exists J i,k such that w i,k > D i,k, then he job released at that instant has response time larger than D. If some jobs don t meet deadlines, this is one of those jobs. here w i,k is the response time of the job. orem: In a fixed-priority system where every job complete ore the next job in the same task is released, a critical insta urs when one of its jobs J i,c is released at the same time wi from every higher-priority task. ntuitively obvious, but proved in the book

10 ing the Critical Instant: Example sider 3 tasks (2.0, 0.6), T2 = (2.5, 0.2), T3 = (3, 1.2) 5 10 sks scheduled using rate-monotonic response times of jobs in T 2 are: 2,1 = 0.8, r 2,2 = 0.3, r 2,3 = 0.2, r 2,4 = 0.2, r 2,5 = 0.8, herefore, the critical instants of T 2 are t = 0 and t = 10 at are the response times of jobs in T 3?

11 g the Critical Instant ing determined the critical instants, show that each job J i,c released at a critical instant, that job and all h rity tasks complete executing before their relative deadlin o, the entire system be schedulable t is: don t simulate the entiree system, simply show that it h rect characteristics following a critical instant his process is called time demandd analysis

12 -Demand Analysis pute the total demand for processor time by a job release ical instant of a task, and by all the higher-priority tasks, a ction of time from the critical instant ck if this demand can be met before the deadline of the job onsider one task, T i, at a time, starting highest priority and workin own to lowest priority ocus on a job, J i, in T i, where the release time, t 0, of that job is a cri nstant of T i t time t 0 + t for t 0, the processor time demand w i (t) for this job igher-priority jobs released in [t 0 0, t ] is:

13 -Demand Analysis pare the time demand, w i (t), with the available time, t: f w i (t) t for some t D i, the job, J i, meets its deadline, t 0 + D i f w i (t) > t for all 0 < t D i then the task probably cannot complete b eadline; and the system likely cannot be scheduled using a fixed pr lgorithm Note that this is a sufficient condition, but not a necessary condition. Simulation may show that the critical instant never occurs in practice, s system could be feasible this method to check that alll tasks are schedulable if relea heir critical instants; if so conclude the entire system can b eduled

14 -Demand Analysis: Example e Monotonic: (3,1), T 2 =(5,2), T 3 =(10,2) time-demand functions 10 t), w 2 (t), and w 3 (t) not above t heir deadline 8 ystem can cheduled Time-demand function, w i (t) J 3,1 startss with a timeof 5 units; demand 2 for itself, 2 for J2,1, 1 for J1,11 Deadline for J 2,1 w 3 (t) w 2 (t) Dead w 1 (t) 0 Deadline for J 1, Tim

15 -Demand Analysis time-demand function w i (t) is a staircase function teps in the time-demand for a task occur at multiples of the period igher-priority tasks he value of w i (t) t linearly decreases from a step until the next ste ur interest is the schedulability of a task, it suffices to chec t) t at the time instants when a higher-priority job is rele schedulability test becomes: ompute w i (t) heck whether w i (t) t is satisfied at any of the instants t = j p k here k = 1, 2,, i j = 1, 2,, ëmin(p i, D i )/p k û

16 -Demand Analysis: Exercise the following tasks: (3,1), T 2 = (5, 1.5), T 3 = (7, 1.25), T 4 = (9, 0.5) raw the time-demand functions etermine if they are RM schedulable one more task (10, 1) raw the time-demand functions etermine if they are RM schedulable

17 -Demand Analysis: Summary e-demand analysis schedulability test is more complex tha schedulable utilization test, but more general orks for any fixed-priority scheduling algorithm, provided the tas ave short response time (i.e. p i < D i ) an be extended to tasks with arbitrary deadlines (see book) nly a sufficient test: guarantees that schedulable results are correc equires further testing to validate a result of not schedulable rnative approach: simulate the behavior of tasks released critical instants, up to the largest period of the tasks till involves simulation, but less complex than an exhaustive simula f the system behavior orst-case simulation method an easily extend the time-demand analysis method for non-preemp

18 tical Factors have assumed that: obs are preemptable at any time obs never suspend themselves ach job has distinct priority he scheduler is event driven and acts immediately se assumptions are often not valid how does this affect t tem?

19 king and Priority Inversion ady job is blocked when it is prevented from executing by er-priority job; a priority inversion is when a lower-priori executes while a higher-priority job is blocked preemptibility ome jobs cannot be pre-empted: Critical section over a resource Some system calls are non-preemptable Disk scheduling f a job becomes non-preemptable, priority inversions may occur, th ay cause a higher priority task to miss its deadline hen attempting to determine if a task meets all of its deadlines, m onsider not only all the tasks thatt have higher priorities, but also onpreemptable regions of lower-prioritdd the blocking time in when calculating if a task is tasks schedulable

20 Suspension and Context Switches -suspension job may invoke an external operation (e.g. request an I/O operatio uring which time it is suspendedd his means the task is no longer strictly periodic again need to tak ccount self-suspension time when calculating a schedule text Switches ssume maximum number of context switches K i for a job in T i is kn ach takes t CS time units ompensate by setting execution time of each job, actual = e i + 2 T cs re if jobs self-suspend, since additional context switches)

21 Scheduling of our previous discussion of priority-driven scheduling w en by events (job release and completion) rnatively, can perform priority-driven scheduling at perio nts (timer interrupts) generated by a hardware clock.e. tick (or time-based) scheduling itional factors to account for in schedulability analysis he fact that a job is ready to execute will not be noticed and acted upon un ext clock interrupt; this will delay the completion of the job ready job that is yet to be noticed by the scheduler must be held somewhe ther than the ready job queue, the pending job queue hen the scheduler executes, it moves jobs in the pending queue to the rea ueue according to their priorities; once in ready queue, the jobs execute in riority order

22 tical Factors ar that non-ideal behaviour can affect the schedulability of tem e touched on how more details later in the module

23 mary e discussed fixed-priority scheduling of periodic tasks: ptimality of RM and DM ore general schedulability tests and time-demand analysis lined practical factors that affect real-world periodic syste