1. Real Time Scheduling Terminologies define Fixed Priority Scheduler
Ref: Real Time System Chapter 2 & 3

2. Your system should sample the temperature sensor reading every 1 ms.
Jobs and Tasks
A job is a unit of work that is scheduled and executed by a system
e.g. computation of a control-law, computation of an FFT on sensor data,
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 .
Your system should sample the temperature sensor reading every 1 ms.
Real Time System

3. Execution Time A job Ji will execute for time ei
This is the amount of time required to complete the execution of Ji when it executes alone and has all the resources it needs
Value of ei depends upon complexity of the job and speed of the processor on which it is scheduled; may change for a variety of reasons:
Conditional branches
Cache memories and/or pipelines
Compression (e.g. MPEG video frames)
Execution times fall into an interval [ei−, ei +]; assume that we know this interval for every hard real-time job, but not necessarily the actual ei
Terminology: (x, y] is an interval starting immediately after x, continuing up to and including
Often, we can validate a system using ei + for each job; we assume ei = ei+ and ignore the interval lower bound
Inefficient, but safe bound on execution time
Real Time System

4. Release and Response Time
Release time – the instant in time when a job becomes available for execution
May not be exact: Release time jitter so ri is in the interval [ri−, ri+]
A job can be scheduled and executed at any time at, or after, its release time, provided its data and control 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
Real Time System

5. Deadline and Timing Constraint
Completion time – the instant at which a job completes execution
Relative deadline – the maximum allowable response time of a job
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
Real Time System

6. Example A system to 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
Real Time System

7. Example
Suppose each job 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
Real Time System

8. Hard vs Soft Real Time
Tardiness – how late a job completes relative to its deadline
lateness = completion time – absolute deadline
tardiness = max(0, lateness)
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 fault; 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
A timing constraint is hard if the user requires validation (formal proof or exhaustive simulation) that the system always meets its timing constraint
Examples: Flight control; Railway signalling; Anti-lock brakes
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
Examples: Stock trading system ; DVD player ; Mobile phone
Real Time System

9. Hard vs Soft Real Time
Note: there may be no advantage in completing a job early
It is often better to keep jitter (variation in timing) in the response times of a stream of jobs small
Timing constraints can be expressed in many ways:
Deterministic
e.g. the relative deadline of every control-law computation is 50 ms; the response time of at most 1 out of 5 consecutive control-law computations exceeds 50ms
Probabilistic
e.g. the probability of the response time exceeding 50 ms is less than 0.2
In terms of some usefulness function
e.g. the usefulness of every control-law computation is at least 0.8
[In practice, usually deterministic constraints, since easy to validate]
Real Time System

10. Modeling Periodic task
A set of jobs that are executed repeatedly at regular time intervals can be modelled as a periodic task
Each periodic task Ti is a sequence of jobs Ji,1, Ji,2, …, Ji,n
The phase of a task Ti is the release time ri ,1 of the first job Ji,1 in the task. It
is denoted by ϕi (“phi”)
The period pi of a task Ti is the minimum length of all time intervals between release times of consecutive jobs
The execution time ei of a task Ti is the maximum execution time of all jobs in the periodic task
The period and execution time of every periodic task in the system are known with reasonable accuracy at all times
The hyper-period of a set of periodic tasks is the least common multiple of their periods: H = lcm(pi) for i = 1, 2, …, n
The time after which the pattern of job release/execution times starts to repeat
Real Time System

11. Modeling Periodic Task
The ratio ui = ei / pi is the utilization of task Ti
The fraction of time a periodic task with period pi and execution time ei keeps a processor busy
The total utilization of a system is the sum of the utilizations of all tasks in a system: U = Σui
We will usually assume the relative deadline for the jobs in a task is equal to the period of the task
It can sometimes be shorter than the period, to allow slack time
< Many useful, real-world, systems fit this model; and it is easy to
reason about such periodic tasks >
Real Time System

12. Responding to External Event
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 modelled 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]
Real Time System

13. Modeling sporadic and areriodic task
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 >
Real Time System

14. Approaches to Real-Time Scheduling
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
time based and
event-based activities,
where the system must adapt to changing conditions and events .
Real Time System

15. Clock Driven Scheduling
Decisions about what jobs execute at what times are made at specific time instants
These instants are chosen before the system begins execution
Usually regularly spaced, implemented using a periodic timer interrupt
Scheduler awakes after each interrupt, schedules the job to execute for the next period, then blocks itself until the next interrupt
Typically in clock-driven systems:
All parameters of the real-time jobs are fixed and known
A schedule of the jobs is computed off-line and is stored for use at runtime; as a result, scheduling overhead at run-time can be minimized
Simple and straight-forward, not flexible
Real Time System

16. Round Robin Scheduling
Regular round-robin scheduling is commonly used for scheduling 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)
Real Time System

17. Priority-Driven Scheduling
Assign priorities to jobs, based on some algorithm
Make scheduling decisions based on the priorities, when events such as releases and job completions occur
Priority scheduling algorithms are event-driven
Jobs are placed in one or more queues; at each event, the ready job with the highest priority is executed
The assignment of jobs to priority queues, along with rules such a whether preemption is allowed, completely defines a priority scheduling algorithm
Priority-driven algorithms make locally optimal decisions about which job to run
Locally optimal scheduling decisions are often not globally optimal
Priority-driven algorithms never intentionally leave any resource idle
Leaving a resource idle is not locally optimal
Real Time System

18. Priority Driven Scheduling
Most scheduling 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
Least slack time first
Etc.
Real Time System

19. RATE Monotonic Algorithm (RM) Assumptions Fixed-priority algorithms
Deadline monotonic
Chapter 6 of Liu Book

20. Assumptions
Focus on well-known priority-driven algorithms for scheduling 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, never intentionally leave a resource idle
Context switch overhead negligibly small; unlimited priority levels
Real Time System

21. Fixed- and Dynamic-Priority Algorithms
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
Jobs in a task may be assigned the same priority (task level fixed priority) or different priorities (task level dynamic-priority)
The priority of each job is usually fixed (job level fixed-priority); but some systems can vary the priority of a job after it has started (job level dynamic-priority)
Job level dynamic-priority usually very inefficient
Real Time System

22. Fixed-Priority Scheduling: Rate-Monotonic
Best known fixed-priority algorithm is rate-monotonic scheduling
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 higher rate have higher priority
Widely studied and used
For example, consider a system of 3 tasks:
T1 = (4, 1) ⇒ rate = 1/4
T2 = (5, 2) ⇒ rate = 1/5
T3 = (20, 5) ⇒ rate = 1/20
Relative priorities: T1 > T2 > T3
Real Time System

23. Example: Rate-Monotonic Scheduling
Real Time System

24. Fixed-Priority Scheduling: Deadline-Monotonic
The deadline-monotonic algorithm 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
Real Time System

25. Schedulability Tests
Simulating schedules 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 for this!
Real Time System

26. Scheduable Utilization
Real Time System

27. Schedulable Utilization of RM
Real Time System

28. Schedulable Utilization of RM
Real Time System

29. Schedulable Utilization of RM
Real Time System

30. Exercise your brain muscle
Assume that you have a system of periodic, independent, pre-emptible tasks to be scheduled on a single processor,
T = {Ti} for i = 1..n,
where Ti = (φi, pi, ei, and Di) for each i.
Real Time System

31. (a) Assume that pi = Di for each i
(a) Assume that pi = Di for each i. What is the schedulability condition of the Rate Monotonic algorithm for this system? Is this a necessary and sufficient condition?
(b) Assume that pi ≤ Di for each i. Under what conditions will the schedulability of the Rate Monotonic algorithm for this system be identical to that stated in response to part (a) above?
Real Time System