Clock Driven Schedulers 4/27/2017 Clock Driven Schedulers Fred Kuhns Applied Research Laboratory Computer Science Washington University

Clock-Driven Approach With periodic tasks, it is possible to statically determine a schedule: cyclic schedule implemented by a cyclic executive. The cyclic schedule is a table listing jobs and their start times (aka decision time). Each job scheduled as a unit and is non-preemptable. Job may be function call, block of instructions, portion of procedure. Cyclic schedule (Table) defines a block of repeatable scheduling decisions where all deadlines and periods are met - Major Cycle. Timing decisions made only at frame boundaries. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Example Timer-Driven Schedule int MajorCycle = 10; int entry = -1; clock_handler () { time_t next_time; current = Table[entry].task; entry = (entry+1) % MajorCycle; next_time = Table[entry].time + gettime(); execute_task(current); if (gettime() > next_time) handle_overload(); return; } t1 T(t1) ... tn T(tn) Table (Cyclic Schedule) Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Creating a Model Major cycle can be divided into a sequence of fixed sized minor cycles (aka frames). Scheduling decisions are only made at frame boundaries. Exact start and completion time of jobs within frame is not known but must know the max computation time Jobs are allocated to specific frames Major cycle time corresponds to a Hyperperiod. If a schedule can not be found for the set of predefined jobs then they may need to be divided into job slices. divide job into a sequence of smaller jobs Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Model Description Periodic task model: N periodic tasks, where N is fixed Parameters of all periodic tasks known a priori assume interrelease time jitter negligible Ji,k (job k of task i) ready at its release time ri,k Major Cycle Minor Cycle (frame) ... T1 T3 T2 T1 T4 T1 T3 T2 f1 f2 fn Cyclic Executive runs in response to a tick event, bar shows time to execute scheduler Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Constructing a Schedule Construct static schedule for a Major Cycle Cyclic Executive repeats this schedule segment There may be resulting idle intervals if so attempt to arrange so they occur periodically Static table lists frame fk and tasks to run tasksk (scheduling block), Cyclic Schedule f1 tasks1 ... ... f5 tasks5 Task = ( r, e) T1 = ( 4, 1) T2 = ( 5, 1.8) T3 = (20, 1) T4 = (20, 2) H = 20 Major Cycle (Hyperperiod) frame 1 frame 2 frame 3 frame 4 frame 5 T1 T3 T2 T1 T4 T2 T1 T2 T1 T1 T2 t = 0 4 8 12 16 20 Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Example Cyclic Executive int MajorCycle = 10; int MinorCycle = 1; int frame=-1; // tick handler, // called at start of frame ce_handler() { time_t next_time = 0; // ensure previous frame completed if (previous execute_scheduler running) handle_overrun(); // error // determine frame and schedule frame = (frame + 1) % MajorCycle; next_time = gettime() + MinorCycle; schedule = CyclicTable[frame].sched; // sequentially run each job in schedule execute_schedule(schedule); // done with this frame return; } execute_schedule (schedule) { job_t job; for each job in schedule execute job return } Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Partitioning Major Cycles into Frames Three tasks: choosing frame size, partitioning jobs into slices (if needed), placing jobs/slices into frames. Frames boundaries (start of frame) cyclic executive performs scheduling, monitoring and enforcement There is no preemption within frame Phase of every task instance is multiple of frame (j·f) first job of task starts on frame boundary, T = j·f. T1 T3 T2 T1 T4 T2 T1 T2 T1 T1 T2 Hyperperiod, Major Cycle Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Frame Size Constraints Every job can start and complete within a frame f ≥ max(ei), 1≤i≤ n Frame size divides H (the Hyperperiod) f divides pi for at least one value of i for a, x and k positive integers: ai·pi = H and x·f = pi  k · f = H Between the release time and deadline of every job there is at least one frame t’ = release time of a job Jij; Dij = relative deadline of job Jij Want t + 2f ≤ t’ + Di or 2f - (t' - t) ≤ Di, but t' - t ≥ gcd(pi, f) if 2f - gcd(pi, f) ≤ Di then 2f - (t' - t) ≤ Dimust be true. If t’ = t then it suffices if f ≤ Di. fk+1 fk fk+2 Jij feasible interval t t' t+f t+2f t'+Di t+3f t'+pi Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Foreground/Background Scheduling aperiodic jobs with periodic jobs Foreground jobs => periodic jobs already discussed background jobs => aperiodic jobs Aperiodic jobs executed within the idle blocks Aperiodic jobs are preemptable May optimize response time by scheduling within schedule slack time (slack stealing). Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Slack Stealing Slack = f – xk where xk = total time allocated to periodic tasks in frame k and f = frame size Requirements may include some minimal aperiodic arrival rate Cyclic Exec executes aperiodic jobs as long as there is slack in the schedule. Periodic jobs must complete by deadline. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Slack Stealing Release times: A1 = 4 A2 = 9.5 A3 = 10.5 Periodic Jobs Only Without Slack stealing A2 A3 A1 A2 A3 With Slack stealing A2 A3 A1 A2 A3 4 8 12 16 20 Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Simplifying Precedence Constraints To accommodate precedence and timing constraints derive a set of effective release times and deadlines Effective release time: no predecessors then equal to its release time. If predecessors then maximum of its own release time and the effective release times of its predecessor. Effective deadline: No successor, then equal to its original deadline. Otherwise minimum of its deadline the effective deadlines of its successors. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Modeling System Modeling the system for an average response time calculation Assume M/G/1 queuing model: Poisson arrival process (exponentially distributed inter-arrival times) General distribution function for service times Infinite queue, FIFO dispatch discipline Single server, single queue nT = # tasks; λi mean arrival rate and ei mean execution time  = mean arrival rate Departure Dispatching Service Server λ = mean arrival rate, μ = mean service rate, Ts = 1/μ (service time) ρ = λ/μ = utilization, w = items in Q, Tw = mean waiting time in Q, q = total number of items in system, Tq = Tw + Ts = total time waiting in system Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Average Response Time ... B1 B2 B3 B4 BN View as one large sample space comprised of the individual aperiodic Task sample spaces (used to calculate average and second moments, E[Bi] and E[Bi2]). Let N = nT in the above diagram. U = total utilization of periodic jobs. So (1-U) is the fraction of processor time available for aperiodic jobs. Thus UA must be < (1-U). Individual events scale by 1/(1-U): eAi = Bi/(1-U) Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Average Response Time Average queuing time inversely proportional to the square of the aperiodic bandwidth (1-U). Can improve average response of some jobs by using priority queues. Average queuing time increases with variance (E[x**2] = E[x] + Variance[x]) Average response time W Average service time Ts i na Averaging queuing time Tw (i/ ) * E[Bi]/(1-U) + W0 / {(1-U)2 [( 1 - UA/(1-U)]} W = i na i * E[Bi2]/2 = W0 Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Wait time versus Aperiodic Utilization Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Scheduling Sporadic Jobs represent as S(d,e): d = deadline, e = execution time have hard deadlines, minimum interrelease times and maximum execution time are not known in advance maximum execution time is known on release jobs are preemptable Apply an acceptance test at run time When job is released, determine if there is a feasible schedule that includes this sporadic job If no feasible schedule, then reject job and notify application of rejection Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Performing an Acceptance Test S(d,e) released at time t in frame x-1: for example an interrupt is received in frame x-1. The deadline d is in frame (y+1) => S must complete before frame y+1 begins Current total slack time available between frames x and y (inclusive) = Qc(x, y) S is rejected if e > Qc(x, y), OR some previously accepted jobs will not meet deadline Order waiting jobs using EDF Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Earliest Deadline First (EDF) EDF: priority driven scheduling algorithm with dynamic task (fixed job) priority assignment. earlier the deadline, higher the priority priorities are assigned on job release Jobs placed in run queue by priority Assumptions: Tasks are preemptable and independent Tasks have arbitrary release times, arbitrary deadlines Single Processor Optimal: EDF can produce a feasible schedule for a set of Jobs J if and only if J has a feasible schedule. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Latest Release Time (LRT) Goes "backwards" in time: Treats release times as deadlines and deadlines as release times. job with latest release time has highest priority Assume jobs are preemptable May leave processor idle when jobs are ready, so not a priority-driven algorithm. Optimal: LRT can produce feasible schedule for a set of jobs J if and only if feasible schedules for J exist. Idle J1, 3 (0, 6] J2, 2 (5, 8] J3, 2 (2, 7] J1 J3 J2 1 4 6 8 Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Least Slack Time First (LST) LST or Maximum Laxity First (MLF) Dispatch job with minimum slack time: smaller slack time, higher priority. Optimal: Can produce feasible schedules for J if and only if feasible schedules for J exist. Requires knowledge of execution times, while EDF does not. Consequently may underutilize processor when using maximum (worst-case) analysis. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Performing and Acceptance Test Beginning of each frame: perform acceptance test on any waiting sporadic tasks Two steps: Determine if sporadic task can complete execution using available slack time (subtract any slack time used by accepted tasks with deadlines before d) Determine if any already accepted sporadic tasks with deadlines after d will be affected Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Implementation: Calculating Slack Time Calculating the available slack time S was released within previous frame, (x - 1) S has deadline in frame (y + 1) so must complete execution no later than frame y Acceptance test performed at start of frame x calculated between frame x and frame immediately preceding deadline, frame y if deadline is in frame x then S can not be scheduled Suffices to know original slack time between all frame pairs within one major cycle, Q(x, y) for x, y in H. Assume x is in major cycle j and y is in major cycle k Q(x,y) = Q(x,F) + Q(1,y) + [(k - 1) - j]Q(1,F); k > j Q(x, y) is known if k = j, y > x. Q(x, x) = is known, slack in current frame Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Accepting S: Step 1 If sporadic jobs are already in system then the available slack time is given by: Qc(x, y) = Q(x, y) - Sum[dkd; (ek - e'k)] slack minus remaining execution time of higher priority tasks. e'k = time job k has already executed The sum is over all jobs with deadline dk  d. If S is accepted Slack before new sporadic job's deadline: Qs = Qc(x, y) – e if job is accepted then store value with job if (Qs < 0) then reject else continue Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

CSE522S – Advanced Operating Systems Accepting S: Step 2 Check all jobs with deadlines after d to verify they will not miss their deadlines. d = deadline of new sporadic task e = execution time of new sporadic task Let Sl = an already accepted sporadic task with deadline dl > d. Let Ql = calculated slack for sporadic tasks in Sl Accept if Step one is valid and the following condition is valid Ql - e  0 for all sporadic jobs with dl>d Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Summary Acceptance Test Scheduler must store the following Precomputed slack table, Q(x, y), {x ,y = 1, 2, ..., F} Completed execution time of accepted sporadic jobs, e'k Current slack (Qs) of every sporadic job Optimality of Cyclic EDF (on-line algorithm) it is optimal compared to other schemes that perform an acceptance test at beginning of frames Not optimal compared to algorithms performing acceptance tests at arbitrary times. However, this may impact the periodic tasks which may be interrupted an arbitrary number of times in order to perform acceptance tests for released sporadic jobs. Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Practical Considerations Frame Overruns Abort job, schedule recovery job Execute unfinished portion as aperiodic job Continue executing job Mode changes: system reconfiguration. Assume periodic jobs are independent Hard-deadline: Soft-deadline: Other Workloads Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Assessing Clock-Driven Scheduling Advantages: Simplicity: account for dependencies and resource contention. No need for synchronization mechanisms. Timing constraints verified or enforced at frame boundaries while minimizing overhead due to context switches and IPC mechanisms. Simple scheduling algorithm to minimize overhead. Minimal impact of asynchronous system processing (interrupts for example) often verification is simple Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems

Assessing Clock-Driven Scheduling Disadvantages: inflexible Model and implementation may be too simple and restrictive Difficult to add new components or change existing system parameters Release times must be fixed Must know all periodic parameters in advance operation modes must be explicitly enumerated and scheduled Fred Kuhns (4/27/2017) CSE522S – Advanced Operating Systems