chapter 3 task assignment and scheduling

1. Chapter 3 Task Assignment and Scheduling 3.1 Introduction 3.2 Rate monotonic analysis 3.3 Other uniprocessor scheduling algorithms 3.4 Task assignment 3.5 Fault-tolerant scheduling

2. Real-Time Systems (Dr Shamala) 2

3. Real-Time Systems (Dr Shamala) 3 Scheduling

4. Real-Time Systems (Dr Shamala) 4 The allocation/scheduling problem can be stated as follows: Given a set of factors affecting allocation/scheduling Tasks (consumes resources) number of tasks, priorities task characteristics periodicity timing constraints task precedence constraints (best described using precedence graph) resource requirements inter-task interactions We are asked to devise a feasible allocation / schedule on a given computer

5. Real-Time Systems (Dr Shamala) 5 Precedence Graph

6. Real-Time Systems (Dr Shamala) 6 Precedence Graph The arrows indicate which task has precedence over the other task. We denote the precedence task set of task T by <(T) that is , (T) indicates which tasks must be completed before Y can begin.

7. Real-Time Systems (Dr Shamala) 7 Precedence Graph (Cont.) <(1) = ? <(2) = {1} <(3) = {1} <(4) = {1} <(5) = {1,2,3} or {2,3} <(6) = {1,3,4} <(7) = {1,3,4,6} <(8) = {1,3,4,6,7}

8. Real-Time Systems (Dr Shamala) 8 Precedence Graph (Cont.) We can also write : i < j to indicate that task Ti must precede task Tj. It can also be written as : j > i The precedence operator is transitive: i< j and j < k ? i < k For economic representation: Only the list of immediate ancestors in the precedence set: E.g. < (5) = {2,3} since <(2) = {1}

9. Real-Time Systems (Dr Shamala) 9 Each task has : Each task requires resources. Eg. Processor execution time, memory or access to a bus Resources examples: Resources may be (depending to its usage): Exclusively held by a task Release Time of a task- the time at which all the data that are required to begin executing the task are available. Deadline � the time at which the task must complete its execution. (Deadline ? maybe hard or soft). Relative deadline = Absolute deadline � release time

10. Real-Time Systems (Dr Shamala) 10 Each task �(cont.) Task Periodic every Pi seconds, the constraints is that it has to run exactly once every period. Every period is generally ? Deadline Sporadic not periodic but has an upper bound on the rate in which it has to be invoked. Irregular intervals Aperiodic Not periodic but has no upper bound

11. Real-Time Systems (Dr Shamala) 11 Precedence constraints inter-task relationship precedence graph <(T) : precedent-task set of task T i < j : task Ti precedes task Tj Resource requirements exclusive nonexclusive

12. Real-Time Systems (Dr Shamala) 12 Characteristics of task assignment/scheduling feasible schedule a valid schedule by which every task completes by its deadline task assignment in case of multiple processors for a set of processors P, time t, set of tasks ?, the schedule S is a function such that S: P � t ? ? S(i, t) : task scheduled to run on processor i at time t online (dynamically) vs offline scheduling (precomputed) Static(doesn�t change within a mode) vs dynamic priority algorithm preemptive vs nonpreemptive scheduling

13. Real-Time Systems (Dr Shamala) 13 Inter-task interactions inter-task communication synchronous asynchronous mutual exclusion problem (synchronization) priority inversion chained blocking deadlock

14. Real-Time Systems (Dr Shamala) 14 Assignment / scheduling problems Most problems pertaining are more than two processors must make do with heuristics. Heuristics are motivated by the fact that uniprocessor scheduling are tractable. Thus, multiprocessor schedule are divided into two (2) steps: 1) assign tasks to processors 2) Run a uniprocessor schedule to schedule the task allocated to each processor. If one or more schedules cannot be feasible, then we must either return to the allocation step and change the allocation or declare that a schedule cannot be found.

15. Real-Time Systems (Dr Shamala) 15 Developing a multiprocessor schedule

16. Real-Time Systems (Dr Shamala) 16 Uniprocessor scheduling algorithms traditional rate-monotonic (RM) rate-monotonic deferred server (DS) earliest deadline first (EDF) precedence and exclusion conditions multiple task versions IRIS tasks increased reward with increased service mode changes Overview

17. Real-Time Systems (Dr Shamala) 17 Multiprocessor scheduling utilization balancing algorithm next-fit algorithm bin-packing algorithm myopic offline scheduling algorithm focused addressing and bidding algorithm assignment with precedence constraints Critical sections Fault-tolerant scheduling

18. Real-Time Systems (Dr Shamala) 18 Notation n number of tasks in task set ci execution time of task ti Ti period of periodic task ti Ii phase of periodic task ti di relative deadline of task ti Di absolute deadline of task ti ri release time of task ti

19. Real-Time Systems (Dr Shamala) 19 Commonly Used Approaches Weighted round-robin approach tasks waiting in the FIFO queue a task with weight wt get wt time slices every round suitable for scheduling real-time traffic in high-speed switched networks a switch downstream can begin to transmit an earlier portion of the message upon receipt of the portion, without having to wait for the arrival of the later portion no need for sorted priority queue ? speedup of scheduling

20. Real-Time Systems (Dr Shamala) 20 Priority-driven approach never leaves any resource idle intentionally greedy scheduling, list scheduling, work-conserving scheduling most scheduling algorithms used in nonreal-time systems are priority-driven preemptive vs. nonpreemptive

21. Real-Time Systems (Dr Shamala) 21 Clock-driven(time-driven) approach tasks and their timing constraints are known a priori except for aperiodic tasks relies on hardware timers a static schedule constructed off-line cyclic schedule: periodic static schedule clock-driven schedule: cyclic schedule for hard real-time tasks foreground/background approach foreground: interrupt-driven scheduling background: cyclic executive (�Big loop�)

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24. Real-Time Systems (Dr Shamala) 24 3.2 Rate Monotonic Analysis Assumptions A1. No nonpreemptible parts in a task, and negligible preemption cost A2. Resource constraint on CPU time only A3. No precedence constraints among tasks A4. All tasks periodic A5. Relative deadline = period

25. Real-Time Systems (Dr Shamala) 25 Rate-Monotonic Scheduling(RMS) Overview rate monotonic priority the higher rate, the higher priority schedulability guaranteed if utilization rate is below a certain limit for feasible schedules fi = 1/Ti : frequency (=rate) ci or Ci : execution time

26. Real-Time Systems (Dr Shamala) 26 3.3 Other Uniprocessor Scheduling Algorithms Period transformation for transient overload a modified form of RM scheduling Dynamic scheduling earliest deadline first scheduling least laxity first scheduling Scheduling of IRIS tasks imprecise computation Scheduling of aperiodic tasks Mode change

27. Real-Time Systems (Dr Shamala) 27 Period Transformation Period transformation for transient overload changes the period to cope with transient overloads (in terms of RM scheduling) actually, to cope with semantic criticality in RM scheduling example tasks: T1: T1 = 12, C1 = 4, C1+ = 7 [Ci+: worst case] T2: T2 = 22, C2 = 10, C2+ = 14 utilization rates: average = 0.79, worst case = 1.22 problem: if T2 is hard rt and T1 is soft (or not), how can we guarantee T2�s deadline in case of transient overload, and T1�s deadline in the average case?

28. Real-Time Systems (Dr Shamala) 28 (continued) solution: boost priority of T2 by reducing its period replace T2 by T2�: T2� = T2 /2, C2� = C2 /2, C2�+ = C2 +/2 an alternative: lower the priority of T1 by lengthening its period in this case, double the value of parameters the new deadline must be ok

29. Real-Time Systems (Dr Shamala) 29 Earliest Deadline First Scheduling Also know as Deadline Monotonic EDF scheduling dynamic priority based, deadline monotonic scheduling Properties EDF is optimal for uniprocessors for periodic tasks with their relative deadline equal to periods: if the total utilization of the task set is no greater than 1, the task set can be feasibly scheduled on a single processor by EDF. Allows preemptions.

30. Real-Time Systems (Dr Shamala) 30 Procedure 1. Sort task instances that require execution in time interval [0, L] in reverse topological order. 2. Initialize the deadline of the kth instance of task Ti to (k-1)Ti + di, if necessary 3. Revise the deadlines in reverse topological order. 4. Select the task with earliest deadline to execute

31. Real-Time Systems (Dr Shamala) 31 Uniprocessor Scheduling of IRIS Tasks Introduction Not necessary to run to completion. Iterative algorithms. Task of this type are known as increased reward with increased service (IRIS) reward function R(x) typically where r(x) is monotonically nondecreasing in x. m, o : execution time of the mandatory and optional parts, respectively

32. Real-Time Systems (Dr Shamala) 32 3.4 Task Assignment Assignment of tasks to processors use heuristics ? cannot guarantee that an allocation will be found that permits all task to be feasibly scheduled. consider communication costs? precedence of task completion. Sometime an allocation algorithm uses communication costs as part of its allocation criterion.

33. Real-Time Systems (Dr Shamala) 33 Objective to balance processor utilization, and proceeds by allocating the tasks one by one and selecting the least utilized processor. Considers running multiple copies for fault-tolerance systems. for each task Ti, do allocate one copy of Ti to each of the ri least utilized processors update the processor allocation to account for the allocation of Ti end do

34. Real-Time Systems (Dr Shamala) 34 Used in conjunction with RM separation of allocation and scheduling simplifies the scheduler to a local one allocation: centralized, scheduler: distributed objectives: to partition a task set so that each partition is scheduled later for execution on a processor by RM scheduling to use as few processors as possible task characteristics each task has constant period and deadline constraints independent, no precedence constraints

35. Real-Time Systems (Dr Shamala) 35 allocation algorithm n tasks ui : utilization factor of Ti Pi,j : set of tasks assigned to a processor Nk : number of class-k processors used so far tasks are divided into M classes such that assigns k class-k tasks to each class-k processor, keeping the utilization factor of the class-M processor less than ln 2

36. Real-Time Systems (Dr Shamala) 36 Algorithm Next-Fit-M for k = 1 to M do set Nk = 1; set i = 1; while i <= n do if Ti is a task from class-k, 1 <= k < M, then assign Ti to Pk,Nk; if Pk,Nk has currently k tasks assigned to it then set Nk = Nk +1 endif else (Ti is a task from class-M) if the total utilization factors of all the tasks assigned to PM,NM is greater than ln2-ui then set NM = NM + 1 endif assign Ti to PM,NM endif set i = i +1 endwhile if Pk,Nk has not task assigned to it then set Nk = Nk -1

37. Real-Time Systems (Dr Shamala) 37 periodic independent preemptible tasks bin-packing problem: assign tasks such that the sum of utilization factors does not exceed 1, and minimize the number of processors needed first fit decreasing algorithm Initialize i to 1. Set U(j) = 0, for all j. (L : a list of tasks with their utilizations sorted in descending order, nT : # tasks ) while i <= nT do Let j = min{k | U(k) + u(i) <= 1}. Assign the i-th task in L to pj Set i = i + 1 . end while

38. Real-Time Systems (Dr Shamala) 38 Myopic Offline Scheduling (MOS) Algorithm Offline Algorithm �given in advance arrival times, execution time and deadline. Non-pre-emptive task Not only processor resources but also others resources such as memory etc. Schedule Tree MOS proceeds by building up a schedule tree. Each node represents an assignment and scheduling of a subset of the tasks. The root of the schedule tree is an empty schedule. Each child of a node consists of a schedule of its parent node, extended by one task. A leaf of this tree consist of the schedule of the entire task set.

39. Real-Time Systems (Dr Shamala) 39 Myopic Offline Scheduling (MOS) Algorithm algorithm i) start with an empty partial schedule ii) determine if the current partial schedule is strongly feasible then proceed; else backtrack iii) extend the current partial schedule by one task (1) apply the heuristic function to the first Nk tasks in the task set (2) choose the task with the smallest heuristic value to extend the current schedule

40. Develop a node if it is strongly feasible. If not feasible, we backtrack that is we mark that node as hopeless and then go back to its parents

41. Real-Time Systems (Dr Shamala) 41 Introduction online distributed environment, loosely coupled both critical and noncritical tasks local scheduler: handles (critical) tasks arriving at a given node global scheduler: schedules noncritical tasks across processor boundary global state

42. Real-Time Systems (Dr Shamala) 42 FAB cont. algorithms for global scheduling to which node the task should be sent noncooperative algorithm-if enough resources for critical yes; else no for non-critical. random scheduling algorithm-if a processor load is exceeding its threshold then another processor is chosen randomly. focused addressing algorithm � overloaded processor checks its surplus info. and selects a processor which it feels it is able to process the task within its deadline. Prob: surplus info may be outdated. bidding algorithm � simultaneous � lightly loaded to bid (Request For Bids) flexible algorithm <-- focused addressing + bidding

43. Real-Time Systems (Dr Shamala) 43 focused addressing algorithm FAS: focused addressing surplus, tunable parameter locally unschedulable tasks sent to the node with the highest surplus ( > FAS) if no such node is found, the task is rejected

44. Real-Time Systems (Dr Shamala) 44 bidding algorithm first, select k nodes with sufficient surplus k: chosen to maximize the chances of finding a node a request-for-bid(RFB) message is sent to these nodes those nodes that receive RFB message calculate a bid ( = likelihood that the task can be guaranteed) send the bid to the bidder node if the bid > minimum bid req�d the bidder sends the task to node that offers the best bid if no good bid available, reject the task

45. Real-Time Systems (Dr Shamala) 45 symbols pi: a processor node with a newly arriving task that is not locally guaranteed ps: a node that is selected by FA algorithm pt: a node that receives RFB message the flexible algorithm (FAB algorithm) pi selects k nodes with sufficient surplus if the largest value of the surplus > FAS the node with that surplus is chosen as focused node(ps) pi sends the task to ps immediately also, pi sends in parallel a RFB message to the remaining k-1 nodes. RFB contains info on ps when a node receives the RFB message it calculates a bid, sends the bid to ps if ps exists

46. Real-Time Systems (Dr Shamala) 46 (continued) when the task reaches ps it first invokes the local scheduler and checks the feasibility if it succeeds, all the bids for the task will be ignored if it fails, ps evaluates the bids, sends the task to the node responding with the highest bid, and sends this info to pi in case there is no focused node, pi will handle the bidding if ps cannot guarantee the task and if there is no good bid available, then corrective actions follow

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48. Real-Time Systems (Dr Shamala) 48 The Buddy Strategy Same as FAB in the sense that if the processor is overloaded it will try to offload some task to lightly loaded processor. However, it differs in the manner in which it finds the lightly loaded tasks: Each processor has 3 thresholds of loading: U:Under (TU), F: full (TF) and T: over (TV) If a processor has a transition from F/T to U it broadcast an announcement to this effect. This broadcast is not to all processors but to a subset and this effect is known as a buddy effect.

49. Real-Time Systems (Dr Shamala) 49 3.5 Fault-Tolerant Scheduling Introduction in case of hardware failure Systems have sufficient reserve capacity and sufficiently fast failure-response mechanism. multiple processors with a set of periodic tasks multiple copies of each version of a task executed in parallel the approach taken : ghost copies of tasks embedded into the schedule need not be identical to the primary copies the tasks concerned are those that were to have been run by the failing processor ghost copies of tasks embedded into the schedule and activated whenever a processor carrying one of their corresponding primary or previously activated ghost copies failsghost copies of tasks embedded into the schedule and activated whenever a processor carrying one of their corresponding primary or previously activated ghost copies fails

50. Real-Time Systems (Dr Shamala) 50 Fault-tolerant schedule should be able to run one or more copies of each version (or iteration) of a task despite the failure of up to nsust processor Output of each fault-tolerant processor has a ghost schedule + 1+ primary schedules makes room for ghosts by shifting primary copies. feasible pair of a ghost schedule and a primary schedule if both schedules can be merged/adjusted to be feasible

51. Real-Time Systems (Dr Shamala) 51 Ghosts each version of a task must have ghost copies scheduled on nsust distinct processors ghosts are conditionally transparent, only if two ghost copies may overlap in the schedule of a processor if no other processor carries the copies of both tasks (that is, if the primary copies of both tasks are not assigned to the same processor) primary copies may overlap the ghosts only if there is sufficient slack time in the schedule to continue to meet all the deadlines

52. Real-Time Systems (Dr Shamala) 52 Algorithm FA1 Ha: assignment procedure, Hs: EDF scheduling procedure 1. Run Ha to obtain a candidate allocation of copies to processors. 2. Run Hs for ghost and primary copies on a processor i. if the resulting schedule is found infeasible, return to step 1 otherwise, record the position of the ghost copies in ghost schedule Gi, and the position of the primary copies in schedule Si. (the primary copies will always be schedule according to S regardless of any ghost happen or not) Limitation: - primary tasks are needlessly delayed when the ghost do not have to be executed. While all task will meet their deadlines, it is frequently best to complete execution of the task early to provide slack time.

53. Real-Time Systems (Dr Shamala) 53 Algorithm FA2 1. Run Ha to obtain a candidate allocation of copies to processors. 2. Run Hs for ghost and primary copies on a processor i. if the resulting schedule is found infeasible, return to step 1 otherwise, record the position of the ghost copies in ghost schedule Gi. Assign static priorities to the primary tasks in the order in which they finish executing. 3. Run a static-priority preemptive scheduler for primary copies with the priorities to obtain Si

54. Real-Time Systems (Dr Shamala) 54 Example ghosts: g4, g5, g6 primaries: h1, h2, h3 h1 h2 h3 g4 g5 g6 release time 2 5 3 0 0 9 execution time 2 2 4 2 2 2 deadline 6 8 15 5 6 12 for the primary copies of g4 and g5 case 1: they are allocated to the same processor case 2: they are on different processors

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