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![Deadlines and Timing Constraints
9
• Completion time – the instant at which a job completes execution
• Relative deadline – the maximum allowable job response time
• Absolute deadline – the instant of time by which a job is required to be
completed (often called simply the deadline)
– absolute deadline = release time + relative deadline
– Feasible interval for a job Ji is the interval ( ri, di ]
• Deadlines are examples of timing constraints](https://image.slidesharecdn.com/unitiv-real-timecharacteristics1-250919052332-96949b26/85/UNIT-IV-REAL-TIME-CHARACTERISTICS-1-pdf-9-320.jpg)
![Sporadic and Aperiodic
1
7
• Many real-time systems are required to respond to external events
• The jobs resulting from such events are sporadic or aperiodic
jobs
– A sporadic job has a hard deadlines
– An aperiodic job has either a soft deadline or no deadline
• The release time for sporadic or aperiodic jobs can be modeled as a
random variable with some probability distribution, A(x)
– A(x) gives the probability that the release time of the job is not later than x
• Alternatively, if discussing a stream of similar sporadic/aperiodic jobs,
A(x) can be viewed as the probability distribution of their inter-
release times
[Note: sometimes the terms arrival time (or inter-arrival time) are used instead of release time, due to
their common use in queuing theory]](https://image.slidesharecdn.com/unitiv-real-timecharacteristics1-250919052332-96949b26/85/UNIT-IV-REAL-TIME-CHARACTERISTICS-1-pdf-17-320.jpg)
![Winter 2010- CS 244 63
Rate Monotonic (RM) Scheduling
z Well-known technique for scheduling independent
periodic tasks [Liu, 1973].
z Assumptions: low period: high priority
y All tasks that have hard deadlines are periodic.
y All tasks are independent.
y di=pi, for all tasks.
y ci is constant and is known for all tasks.
y The time required for context switching is negligible](https://image.slidesharecdn.com/unitiv-real-timecharacteristics1-250919052332-96949b26/85/UNIT-IV-REAL-TIME-CHARACTERISTICS-1-pdf-63-320.jpg)
UNIT IV - REAL-TIME CHARACTERISTICS (1).pdf
- 1. EMBEDDED SYSTEM DESIGN/EEE18R423 Presented By Mr.S.Kalimuthu Kumar Asst. Prof./EEE KalasalingamAcademy of Research & Education
- 2. UNIT IV (Analyzethe different scheduling algorithm CO5) 1 • Clock driven approach- weighted round robin approach 2 • Priority driven approach -Dynamic versus static systems - 3 • Effective release times and deadlines - optimality of the Earliest Deadline First (EDF) algorithm 4 • Challenges in validating timing ,constraints in priority driven systems 5 • Off-line versus on-line scheduling.,Task Scheduling. 2
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- 4. A Real timesystem is a type of hardware or software that operates with a time constraint It is one that must process information and produce a response within a specified time, else risk severs consequences ,including failure that is ,in a system with a real time constraint . It is no good to have the correct action or the correct answer after a certain dead line Real time system
- 5. Type of Realtime system Hard Real time(Ex. Air Bag control) A system that is designed to meet strict timing requirements is often referred to as a Hard RTS Soft Real time(Ex. Banking ATM) A System for which occasional timing failures are acceptable is often referred to as Soft RTS 5
- 6. Jobs and Tasks 6 •A job is a unit of work that is scheduled and executed by a system – e.g. computation of a control-law, transmission of a data packet, retrieval of a file • A task is a set of related jobs which jointly provide some function – e.g. the set of jobs that constitute the “maintain constant altitude” task, keeping an airplane flying at a constant altitude
- 7. Execution Time • Ajob Ji will execute for time ei –This is the amount of time required to complete the execution of when it executes alone and has all the resources it needs –Complexity of job , speed of processor, scheduler 7
- 8. Release and ResponseTime • Release time – the instant in time when a job becomes available for execution – A job can be scheduled and executed at any time at, or after, its release time, provided its resource dependency conditions are met • Response time – the length of time from the release time of the job to the time instant when it completes – Not the same as execution time, since may not execute continually 8
- 9. Deadlines and TimingConstraints 9 • Completion time – the instant at which a job completes execution • Relative deadline – the maximum allowable job response time • Absolute deadline – the instant of time by which a job is required to be completed (often called simply the deadline) – absolute deadline = release time + relative deadline – Feasible interval for a job Ji is the interval ( ri, di ] • Deadlines are examples of timing constraints
- 10. Example 1 0 • A systemto monitor and control a heating furnace • The system takes 20ms to initialize when turned on • After initialization, every 100 ms, the system: – Samples and reads the temperature sensor – Computes the control-law for the furnace to process temperature readings, determine the correct flow rates of fuel, air and coolant – Adjusts flow rates to match computed values • The periodic computations can be stated in terms of release times of the jobs computing the control-law: J0, J1, …, Jk, … – The release time of Jk is 20 + (k × 100) ms
- 11. Example 1 1 • Suppose eachjob must complete before the release of the next job: – Jk’ s relative deadline is 100 ms – Jk’ s absolute deadline is 20 + ((k + 1) × 100) ms • Alternatively, each control-law computation may be required to finish sooner – i.e. the relative deadline is smaller than the time between jobs, allowing some slack time for other jobs – Slack time : the difference between the completion time and the earliest possible completion time
- 12. 13 Hard vs. SoftReal-Time Systems • If a job must never miss its deadline, then the system is described as hard real-time A timing constraint is hard if the failure to meet it is considered a fatal error; this definition is based upon the functional criticality of a job A timing constraint is hard if the usefulness of the results falls off abruptly (or may even go negative) at the deadline – If some deadlines can be missed occasionally, with acceptably low probability, then the system is described as soft real-time – This is a statistical constraint usefulnes s 1 deadline SOFT HARD
- 13. Examples: Hard &Soft Real-Time Systems 1 3 • Hard real-time: – Flight control – Railway signaling – Anti-lock brakes – Etc. • Soft real-time: – Stock trading system – DVD player – Mobile phone – Etc. Can you think of more examples? Is the distinction always clear cut?
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- 15. Periodic Tasks 1 5 • PeriodicTask - a set of jobs that are executed repeatedly at regular time intervals
- 16. Hyper-Periodic Tasks 1 6 • Thehyper-period of a set of periodic tasks is the least common multiple of their periods: – H = LCM(pi) for i = 1, 2, …, n – Time after which the pattern of job release/execution times starts to repeat, limiting analysis needed • Example: T1 : p1 = 3, e1 = 1 T2 : p2 = 5, e2 = 2
- 17. Sporadic and Aperiodic 1 7 •Many real-time systems are required to respond to external events • The jobs resulting from such events are sporadic or aperiodic jobs – A sporadic job has a hard deadlines – An aperiodic job has either a soft deadline or no deadline • The release time for sporadic or aperiodic jobs can be modeled as a random variable with some probability distribution, A(x) – A(x) gives the probability that the release time of the job is not later than x • Alternatively, if discussing a stream of similar sporadic/aperiodic jobs, A(x) can be viewed as the probability distribution of their inter- release times [Note: sometimes the terms arrival time (or inter-arrival time) are used instead of release time, due to their common use in queuing theory]
- 18. Modelling Sporadic andAperiodic Tasks 1 8 • A set of jobs that execute at irregular time intervals comprise a sporadic or aperiodic task – Each sporadic/aperiodic task is a stream of sporadic/aperiodic jobs • The inter-arrival times between consecutive jobs in such a task may vary widely according to probability distribution A(x) and can be arbitrarily small • Similarly, the execution times of jobs are identically distributed random variables with some probability distribution B(x) ⇒Sporadic and aperiodic tasks occur in some real-time systems, and greatly complicate modelling and reasoning
- 19. Scheduling 1 9 • Jobs scheduledand allocated resources according to a chosen set of scheduling algorithms and resource access-control protocols – Scheduler implements these algorithms • A scheduler specifically assigns jobs to processors • A schedule is an assignment of all jobs in the system on the available processors. • A valid schedule satisfies the following conditions: – Every processor is assigned to at most one job at any time – Every job is assigned at most one processor at any time – No job is scheduled before its release time – The total amount of processor time assigned to every job is equal to its maximum or actual execution time – All the precedence and resource usage constraints are satisfied
- 20. Scheduling 2 0 • A validschedule is also a feasible schedule if every job meets its timing constraints. – Miss rate is the percentage of jobs that are executed but completed too late – Loss rate is the percentage of jobs that are not executed at all • A hard real time scheduling algorithm is optimal if the algorithm always produces a feasible schedule if the given set of jobs has feasible schedules • Many scheduling algorithms exist: main focus of this module is understanding real-time scheduling
- 21. Approaches to Real-TimeScheduling 2 1 Different classes of scheduling algorithm used in real-time systems: •Clock-driven – Primarily used for hard real-time systems where all properties of all jobs are known at design time, such that offline scheduling techniques can be used •Weighted round-robin – Primarily used for scheduling real-time traffic in high-speed, switched networks •Priority-driven – Primarily used for more dynamic real-time systems with a mix of timebased and event- based activities, where the system must adapt to changing conditions and events Look at the properties of each in turn…
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- 23. Clock-Driven Scheduling Primarily usedfor hard real time system where all properties of all jobs are known at design time Offline scheduling Deterministic systems Restricted periodic task Aperiodic jobs may exist There is no sporadic jobs It is simple & straight –forward, not flexible. 23
- 24. Clock-driven or time-drivenapproach We refer to a periodic task Ti with phase φi , period pi , execution time ei , and relative deadline Di by the 4-tuple (φi , pi , ei , Di ). For example, (1, 10, 3, 6) is a periodic task whose phase is 1, period is 10, execution time is 3, and relative deadline is 6. 24
- 25. Example of cyclicschedule consider a system with four independent periodic tasks. They are T1 = (4, 1), T2 = (5, 1.8), T3 = (20, 1), T4 = (20, 2). Hyper-period H=20(4X5=20)=LCM 25
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- 31. Clock-driven Scheduling: Advantages 3 1 •Conceptual simplicity • Relatively easy to validate, test and certify
- 32. Clock-driven Scheduling: Disadvantages 3 2 •Inflexible • Other disadvantages: –Release times of all jobs must be fixed –The treatment of aperiodic jobs is very primitive
- 33. Weighted Round -Robin Mechanism WRR assumes an average packet length, then computes a normalized, weighted number of packets to be emitted by each queue in turn, based on the weight assigned to each queue.
- 34. Weighted Round-Robin Scheduling 3 4 •Regular time-shared applications – Every job joins a FIFO queue when it is ready for execution – When the scheduler runs, it schedules the job at the head of the queue to execute for at most one time slice • Sometimes called a quantum – typically O(tens of ms) – If the job has not completed by the end of its quantum, it is preempted and placed at the end of the queue – When there are n ready jobs in the queue, each job gets one slice every n time slices (n time slices is called a round) – Only limited use in real-time systems
- 35. Weighted Round-Robin Scheduling 3 5 •In weighted round robin each job J i is assigned a weight w i; the job will receive w i consecutive time slices each round, and theduration of a round is – Equivalent to regular round robin if all weights equal 1 – Simple to implement, since it doesn’t require a sorted priority queue • Partitions capacity between jobs according to some ratio n i w i1
- 36. Weighted Round-Robin Scheduling 3 6 •By giving each job a fixed fraction of the processor time, a round- robin scheduler may delay the completion of every job • Weighted round-robin is primarily used for real-time networking • The simplicity of these algorithms can be useful for traffic scheduling in very high speed networks
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- 38. Conventional WRR z Ina WRR scheduler, tasks are performed in a cyclic order, in which the time a task can execute within each round is proportional to the weight assigned to it. 38
- 39. Priority-Driven Scheduling 3 9 • Mostscheduling algorithms used in non real-time systems are priority-driven – First-In-First-Out – Last-In-First-Out – Shortest-Execution-Time-First – Longest-Execution-Time-First • Real-time priority scheduling assigns priorities based on deadline or some other timing constraint: – Earliest deadline first(EDF) – Least slack time first(LST) – Etc. Assign priority based on release time Assign priority based on execution time
- 40. Priority Scheduling Basedon Deadlines 4 0 • Earliest deadline first (EDF) – Assign priority to jobs based on deadline – Earlier the deadline, higher the priority – Simple, just requires knowledge of deadlines • Least Slack Time first (LST) – A job J i has deadline d i, execution time e i, and was released at time ri – At time t < d i: • Remaining execution time t rem = e i - (t – ri) • Slack time t slack = d i – t – trem – Assign priority to jobs based on slack time, t slack – The smaller the slack time, the higher the priority – More complex, requires knowledge of execution times and deadlines • Knowing the actual execution time is often difficult a priori, since it depends on the data, need to use worst case estimates (⇒ poor performance) ei di ri t tREM
- 41. Dynamic vs. StaticSystems 4 1 • If jobs are scheduled on multiple processors, and a job can be dispatched from the priority run queue to any of the processors, the system is dynamic • A job migrates if it starts execution on one processor and is resumed on a different processor • If jobs are partitioned into subsystems, and each subsystem is bound statically to a processor, we have a static system • Expect static systems to have inferior performance (in terms of overall response time of the jobs) relative to dynamic systems – But it is possible to validate static systems, whereas this is not always true for dynamic systems – For this reason, most hard real time systems are static
- 42. Effective Release Timesand Deadlines 4 2 • Sometimes the release time of a job may be later than that of its successors, or its deadline may be earlier than that specified for its predecessors • This makes no sense: derive an effective release time or effective deadline consistent with all precedence constraints, and schedule using that – Effective release time • If a job has no predecessors, its effective release time is its release time • If it has predecessors, its effective release time is the maximum of its release time and the effective release times of its predecessors – Effective deadline • If a job has no successors, its effective deadline is its deadline • It if has successors, its effective deadline is the minimum of its deadline and the effective deadline of its successors
- 43. Validating Priority-Driven Scheduling 4 3 •Priority-driven scheduling has many advantages over clock-driven scheduling – Better suited to applications with varying time and resource requirements, since needs less a priori information – Run-time overheads are small • But not widely used until recently, since difficult to validate – Scheduling anomalies can occur for multiprocessor or non-preemptable systems, or those which share resources • Reducing the execution time of a job in a task can increase the total response time of the task (see book for example) • Not sufficient to show correctness with worse-case execution times, need to simulate with all possible execution times for all jobs comprising a task – Can be proved that anomalies do not occur for independent, preemptable, jobs with fixed release times executed using any priority-driven scheduler on a single processor • Various stronger results exist for particular priority-driven algorithms
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- 45. Lecture Outline 4 5 • Assumptions •Fixed-priority algorithms – Rate monotonic – Deadline monotonic • Dynamic-priority algorithms – Earliest deadline first – Least slack time • Relative merits of fixed- and dynamic-priority scheduling • Schedulable utilization and proof of schedulability
- 46. Assumptions 4 6 • Priority-driven schedulingof periodic tasks on a single processor • Assume a restricted periodic task model: – A fixed number of independent periodic tasks exist • Jobs comprising those tasks: – Are ready for execution as soon as they are released – Can be pre-empted at any time • Never suspend themselves • New tasks only admitted after an acceptance test; may be rejected • The period of a task defined as minimum inter-release time of jobs in task – There are no aperiodic or sporadic tasks – Scheduling decisions made immediately upon job release and completion • Algorithms are event driven, not clock driven • Never intentionally leave a resource idle – Context switch overhead negligibly small; unlimited priority levels
- 47. Dynamic versus StaticSystems 4 7 • In static systems, – Jobs are partitioned into subsystems, each subsystem bound statically to a processor – The scheduler for each processor schedules the jobs in its subsystem independent of the schedulers for the other processors – Priority-driven uniprocessor systems are applicable to each subsystem of a static multiprocessor system • In dynamic systems, – Jobs are scheduled on multiple processors, and a job can be dispatched to any of the processors – Difficult to determine the best- and worst-case performance of dynamic systems, so most hard real-time systems built are static • In most cases, the performance of dynamic systems is superior to static system • In the worst case, the performance of priority-driven algorithm can be very poor
- 48. Fixed- and Dynamic-PriorityAlgorithms 4 8 • A priority-driven scheduler is an on-line scheduler – It does not pre-compute a schedule of tasks/jobs: instead assigns priorities to jobs when released, places them on a run queue in priority order – When pre-emption is allowed, a scheduling decision is made whenever a job is released or completed – At each scheduling decision time, the scheduler updates the run queues and executes the job at the head of the queue • Assignment of priority – Fixed-priority algorithm : to assign the same priority all jobs in each task – Dynamic-priority algorithm : to assign different priorities to the individual jobs in each task. Once assigned, the priority of the job does not change (job-level fixed- priority) – Job level dynamic-priority : to vary the priority of a job after it has started. It is usually very inefficient
- 49. Rate Monotonic Scheduling(RM) • Best known fixed-priority algorithm • Assigns priorities to tasks based on their periods The shorter the period, the higher the priority The rate (of job releases) is the inverse of the period, so jobs with shorter period have higher priority 4 9 – T1 = (4,1) – T2 = (5,2) – T3 = (20,5) ⇒ rate = 1/4 ⇒ rate = 1/5 ⇒ rate = 1/20 – Relative priorities: T1 > T2 > T3 • Very widely studied and used • For example, consider a system of 3 tasks:
- 50. Example: Rate MonotonicScheduling 0 5 10 15 20 T1 T1 T1 T1 T1 T2 T2 T2 T2 T2 T3 T3 T3 T3 T1 T2 0 5 10 15 20 T1 T1 T2 T2 T2 T2 T1 T2 T3 T1 T3 T1 T3 T3 T1 T2 5 0
- 51. Deadline Monotonic Scheduling(DM) 5 1 • To assigns task priority according to relative deadlines – the shorter the relative deadline, the higher the priority • When relative deadline of every task matches its period, then rate monotonic and deadline monotonic give identical results • When the relative deadlines are arbitrary: – Deadline monotonic can sometimes produce a feasible schedule in cases where rate monotonic cannot – But, rate monotonic always fails when deadline monotonic fails – Deadline monotonic preferred to rate monotonic • if deadline ≠ period
- 52. Deadline Monotonic Scheduling(DM) z Task Ti: (ei, pi, di); with relative deadline di <= pi z Assigns priority based on di; smaller the di, higher the priority z Similar to RMS exact analysis, except the ordering of tasks is based on di instead of pi z Example: (ei,pi,di): (3,20,7), (2,5,4), (2,10,9). This task set is schedulable even though Sum(ei/di) > 1. z DMS is also an optimal fixed-priority scheduling algorithm; it is a generalization of RMS 52
- 53. Example: Deadline Monotonic •T1 (50,50,25,100), T2 (0, 62.5, 10, 20), T3 (0,125,25,50) – Relative priority : T2 > T3 > T1 J2,2 J2,3 J2,4 J2,5 J1,1 J1,2 J1,3 J1,4 J2,1 0 50 100 150 200 250 J3,1 J3, 2 J1,1 J2,2 J2,3 J2,4 J2,5 J2,1 J3,1 J3,2 J1,1 J1,2 J1,3 J1,4 J1,1 5 3
- 54. Dynamic-Priority Algorithms 5 4 • Earliestdeadline first (EDF) – To assign priorities to jobs in the tasks according to their absolute deadline • Least slack time first (LST) – To check all ready jobs each time a new job is released and – To order the new job and the existing jobs on their slack time – Two variations: • Strict LST – scheduling decisions are made also whenever a queued job’s slack time becomes smaller than the executing job’s slack time – huge overheads, not used • Non-strict LST – scheduling decisions made only when jobs release or complete • First in, first out (FIFO) – Job queue is first-in-first-out by release time • Last in, first out (LIFO) – Job queue is last-in-first-out by release time • Focus on EDF as commonly used example
- 55. Example: EDF 5 5 • T1(2, 0.9), T2 (5, 2.3) J1,1 J2,1 0 2 4 6 8 10 J1,2 J1,3 J1,4 J1,5 J2,2 J2,1 J2,2 J2,2
- 56. Relative Merits 5 6 • Fixed-and dynamic-priority scheduling algorithms have different properties; neither appropriate for all scenarios • Algorithms that do not take into account the urgencies of jobs in priority assignment usually perform poorly – E.g FIFO, LIFO • The EDF algorithm gives higher priority to jobs that have missed their deadlines than to jobs whose deadline is still in the future – Not necessarily suited to systems where occasional overload unavoidable • Dynamic algorithms like EDF can produce feasible schedules in cases where RM and DM cannot. However, it is difficult for the dynamic algorithms to predict which task will miss their deadlines during overloads. – But fixed priority algorithms often more predictable, lower overhead
- 57. Example: Comparing Different Algorithms 5 7 •Compare performance of RM, EDF, LST and FIFO scheduling • Assume a single processor system with 2 tasks: – T1 = (2, 1) – T2 = (5, 2.5) H = 10 • The total utilization is 1.0 ⇒ no slack time – Expect some of these algorithms to lead to missed deadlines! – This is one of the cases where EDF works better than RM/DM
- 58. Example: RM, EDF,LST and FIFO 5 8 • Demonstrate by exhaustive simulation that LST and EDF meet deadlines, but FIFO and RM don’t
- 59. Schedulability Tests 5 9 • Simulatingschedules is both tedious and error-prone… can we demonstrate correctness without working through the schedule? • Yes, in some cases. This is a schedulability test – A test to demonstrate that all deadlines are met, when scheduled using a particular algorithm – An efficient schedulability test can be used as an on-line acceptance test; clearly exhaustive simulation is too expensive
- 60. Task scheduling z Jobsscheduled and allocated resources according to a chosen set of scheduling algorithms and resource access-control protocols z – Scheduler implements these algorithms z • A schedule is an assignment of all jobs in the system on the available processors. z • A valid schedule satisfies the following conditions: z – Every processor is assigned to at most one job at any time z – Every job is assigned at most one processor at any time z – No job is scheduled before its release time z – The total amount of processor time assigned to every job is equal to its maximum or actual execution time 60
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- 62. Online- and offlinescheduling: y Online scheduling is done at run-time based on the information about the tasks arrived so far. y Offline scheduling assumes prior knowledge about arrival times, execution times, and deadlines. 62
- 63. Winter 2010- CS244 63 Rate Monotonic (RM) Scheduling z Well-known technique for scheduling independent periodic tasks [Liu, 1973]. z Assumptions: low period: high priority y All tasks that have hard deadlines are periodic. y All tasks are independent. y di=pi, for all tasks. y ci is constant and is known for all tasks. y The time required for context switching is negligible
- 64. Winter 2010- CS244 64 Example: RM-generated schedule T1 preempts T2 and T3. T2 and T3 do not preempt each other. Period Execution Time T1: 2 0.5 T2: 6 2 T3: 6 1.75
- 65. Summary 6 5 Key points: • Differentpriority scheduling algorithms – Earliest deadline first, least slack time, rate monotonic, deadline monotonic – Each has different properties, suited for different scenarios • Scheduling tests, concept of maximum schedulable utilization – Examples for different algorithms