Priority Driven Scheduling

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BITS PilaniPilani | Dubai | Goa | Hyderabad

BITS C 553

Chapter 6 and 7Swati Keskar


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BITS PilaniPilani | Dubai | Goa | Hyderabad

Real-Time Systems : Scheduling


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BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Plan of The Lecture

September 21, 2013 Swati Keskar 1-3

Priority-driven scheduling

Scheduling aperiodic jobs


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Priority-Driven scheduling

Before starting the discussion, we assume that

The tasks are independent

There are no aperiodic and sporadic jobs

Job is ready for execution as soon as it is released Jobs are preemptible and never suspends itself

Scheduling decisions are made immediately upon job

releases and completion

Context switch overhead is negligible

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Priority-Driven scheduling

It is an on-line scheduler, does not precompute the

schedule

It assigns the priorities to the job after they are released

and places the jobs in ready queue

Two main classifications

Fixed priority: assigns the same priority to all the jobs in

each task Dynamic priority: assigns different priorities to the

individual jobs in each task



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Fixed Priority Algorithms

Rate-Monotonic Algorithm RMA

shorter the period, the higher the priority i.e. higher the

rate of occurrence, higher the priority

Deadline-Monotonic Algorithm DMAshorter the relative deadline, higher the priority



7/49BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Example

Consider a task set T1(7,3) , T2(12,3), T3(20,5)

September 21, 2013 7Swati Keskar



Dynamic Priority algorithms

Earliest Deadline First (EDF)

assigns the priority to individual jobs in the tasks

according to their absolute deadlines

LeastSlack-Time-first (LST)the scheduler checks the slacks of al the ready jobs

each time a new job is released then the smaller the

slack, the higher the priority

FIFO, LIFO etc




Schedulable Utilization

A scheduling algorithm can feasibly schedule any set of

periodic tasks on a processor if the total utilization of the

tasks is equal to or less than the schedulable utilization

of the algorithm

Higher the schedulable utilization of an algorithm , the

better the algorithm

A scheduling algorithm whose schedulable utilization is

equal to 1 is an optimal algorithm




EDF Algorithm

A system T of independent, preemptable tasks with

relative deadlines equal to their respective periods can

be feasibly scheduled on one processor if and only if its

total utilization is equal to or less than 1

ek

UEDF = ---------------- 1

min(Dk,pk)




RMA and DMA

A system of simply periodic, independent, preemptible

tasks whose relative deadlines are equal to or larger

than their periods is schedulable on one processor

according to the RM algorithm if and only if its total

utilization is equal to or less than 1




Schedulability Test

Schedulability test for tasks with short response times ie

where the response times of the jobs are smaller than or

equal to their respective periods

Every job completes before the next job in the same task

is released

We have to the critical instant




Critical Instant

A critical instant of a task Ti is a time instant which is

such that the job in Ti released at the instant has the

maximum response time.

This maximum response time is called Worst Case

Execution Time and is denoted by Wi

Theorem: In a fixed priority system where every job

completes before the next job in the same task is

released, a critical instant of any task Ti occurs when one

of its job Ji,c is released at the same time with a job inevery higher priority task




Time Demand Analysis

To determine whether a task can meet all its deadlines,

we have to compute the total demand for processor time

by a job released at a critical instant of the task and by

all the higher priority tasks at that critical instant

We will then check whether this demand can be met

before the deadline of the job

This test is called Time Demand analysis

Wi(t) = ei + t/pk ek for 0< t pi

This Wi(t) t for some t Di




Example

A task set T1(7,3); T2(12,3) and T3(20,5) is Given. It is

scheduled by using Rate Monotonic Algorithm. Check its

schedulability.




Busy Interval

Here is a schedulability test for fixed-priority tasks witharbitrary response time

When relative deadline are larger than their respectiveperiods, we have to determine the schedulability

Approach is find the busy interval and then apply timedemand analysis test

A level-i busy interval (t0,t ] starts at an instant t0 when

All jobs in Ti released before the instant have completed

A job in Ti is releasedThe interval ends at the first instant t after to when all jobs

in Ti released since t0 are complete




Sufficient Schedulability condition

Schedulable utilization of RM and DM Algorithms for

tasks with Di = Pi gives us a flexible design guidelines for

the choices of the periods and execution times of the

tasks

Theorem : A system of n independent, preemptible

periodic tasks with relative deadlines equal to their

respective periods can be feasibly scheduled on a

processor according to the RMA if its total utilization U is

less than or equal to

URM(n) = n(21/n -1) and U URM




URM as a Function of Task Parameters

Schedulable utilization as a function task utilization

Schedulable utilization of simply periodic tasks

Period ratio

Values of periods Tasks with arbitrary relative deadlines




Practical Factors

Assumptions we have made at the starting are not

always valid. Considering the practical factors, blocking

and priority inversion has to be discussed

Nonpreemptivity

Self suspension

Context switches

Limited priority levels

Tick Scheduling




Tick Scheduling

We are assuming that the scheduler is event-driven

This assumption is always not valid, sometimes the scheduler

is time-driven

Scheduling decisions are made at these time instants called

clock interrupts

This method is also called time-based scheduling and

scheduler executes only at clock interrupts




Example



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Scheduling Aperiodic and

Sporadic Jobs

We assume that the operating system maintains the priority

queue.

The ready periodic tasks are placed in the periodic task queue

according to their priority assigned by any one of the

algorithms

Each accepted sporadic job is assigned a priority and is placed

in priority queue

Each newly arrived aperiodic job is placed in the aperiodic job

queue



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Alternative approaches

Background execution

Polled execution

Interrupt driven execution



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Background Execution

Aperiodic jobs are scheduled and executed only at times

when there is no periodic or sporadic job ready for execution

Always produces correct schedules

Simple to implement

Drawback is that the execution of aperiodic jobs is delayed

and response time is prolonged



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Interrupt Driven Execution

Whenever an aperiodic job arrives, the execution of periodic

tasks are interrupted and the aperiodic job is executed.

In this case, aperiodic job may have the shortest possible

response time

But it has main disadvantage that if aperiodic job always

execute as soon as possible ,periodic task may miss some

deadlines



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Polling Server

A poller or polling server is a periodic task whose polling

period is ps and es is its execution time

The poller is ready for execution periodically and is scheduled

together with the periodic tasks in the system

When it executes, it examines the aperiodic job queue

If the queue is nonempty, the poller executes the job at the

head of the queue

Server suspends its execution when either budget is

exhausted or when the queue becomes empty



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Polling Server

The main disadvantage of poling server is that if at the

beginning of a polling period the poller finds the aperiodic job

queue empty , it suspends immediately

It will not be ready for execution and able to examine the

queue again until the next polling period



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Periodic Server

The periodic server is nothing but a periodic task created for

the purpose of executing aperiodic jobs

It has period ps and execution time es which is called as

execution budget or simply budget

The ratio us = es/ps is the size of the server

At the beginning of each period, the budget of the poller is set

to es i.e. its budget is replenished



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Periodic Server

The periodic server is backlogged whenever the aperiodic job

queue is nonempty and there is at least an aperiodic job to be

executed by the server

The server is idle when the queue is empty

The server is eligible for execution only when it is backlogged

and budget

When the server is scheduled and executes aperiodic jobs, it

consumes its budget at the rate of one per unit time

The server budget becomes exhausted when the budget

becomes zero



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Bandwidth-preserving Servers

If we can preserve the execution budget of the poller when it

finds an empty queue and allow it to execute later in the

period if any aperiodic job arrives, we can improve the

response time of aperiodic job

Algorithms that improve the polling approach in ths mannerare called bandwidth preserving server algorithm

These are periodic servers, each type of server is defined by a

set of consumption and replenishment rules



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Types of bandwidth-preserving servers

Deferrable servers

Sporadic servers

Constant utilization/total bandwidth servers and weightedfair-queuing servers

Bandwidth-preserving Servers



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Deferrable servers

Consumption rule: The execution budget of the server is

consumed at the rate of one per unit time whenever the

server executes

Replenishment rule : The execution budget of the server is set

to es at time instants kpkfor k = 0,1,2



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Schedulability with deferrable Server

Time demand analysis can be used to determine whether all

the periodic tasks remain schedulable in the presence of a

deferrable server (highest priority)

The time demand function of the task Ti in presence of

deferrable server is given by



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Schedulable Utilization

Schedulability of a fixed-priority system in which a deferrable

server is scheduled at an arbitrary priority cannot be assured

Only exception is when the deferrable server has shortest

period in a system of n tasks and the system is scheduled rate-

monotonically



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Theorem for Schedulable Utilization

Consider a system of n independent, preemptible periodic

tasks whose periods satisfy the inequalities

ps < p1 < p2< < pn < 2ps and pn > ps + es and whose relative

deadlines are equal to their respective periods.

This system is schedulable rate-monotonically with a

deferrable server (ps, es) if their total utilization is less than or

equal to



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When the servers period is arbitrary, we can use URM(n) to

determine whether each periodic task Ti is schedulable if the

periodic tasks and the server are scheduled rate-

monotonically

We can treat additional es units of time as additional blockingtime of the task Ti. Ti is surely schedulable if

Theorem for Schedulable Utilization



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Schedulability with deadline-driven systems

A periodic task Ti in a system of n independent, preemptive

periodic tasks is schedulable with a deferrable server with

period ps, execution budget es and utilization us, according to

the EDF algorithm if



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Sporadic Servers

Improved version of deferrable servers

The consumption and replenishment rules of this server

ensure that each sporadic server with period ps and budget es

never demands more processor time than the periodic task

(ps,es) in any time interval

We can treat the sporadic server exactly like the periodic task

when we check for the schedulability of the system

A system of periodic tasks containing a sporadic server may be

schedulable while the same system containing a deferrableserver with same parameters is not



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Simple Sporadic Server

Consumption rules : at any time t after tr ie replenishment

time, the servers budget is consumed at the rate of 1 unit per

time until the budget is exhausted when either one of the

following conditions are true

C1 : The server is executing

C2: The server has executed since tr and END


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Replenishment Rules

Replenishment rules of Simple Fixed-Priority-Sporadic server

are

R1 : Initially when the system begins execution and each time

when the budget is replenished, the execution budget = es

and tr = the current time

R2: At the time tf(first instant after tr when server begins

execution), if END = tf, te = max( tr, BEGIN). If END < tf,

te=tf. The next replenishment time is set at te+ps



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Replenishment Rules

R3 : The next replenishment occurs at the next replenishment

time, except under the following conditions

If the next replenishment time te + ps is earlier than tf, the

budget is replenished as soon as it is exhausted

If the system T becomes idle before the next replenishment

time te + ps , and becomes busy again at tb, the budget is

replenished at min( te+ps, tb).



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Scheduling of Sporadic Jobs

The scheduler performs an acceptance test on each sporadic

job upon its arrival

The acceptance tests are performed on sporadic jobs in the

EDF order

Once accepted, sporadic jobs are ordered among themselves

in the EDF order



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Acceptance Test

For deadline-driven system

For first sporadic job S (t,d,e), the scheduler accepts S if its

density e/(d-t) < 1-

For new sporadic jobs , the scheduler accepts the job S if

e / (d t) + s,k 1- for all k = 1,2



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For fixed-priority systems

For first sporadic job, find slack time

s,1(t) = (ds,1-t)/ps es es,1 0

For next sporadic jobs, the scheduler computes the slack

s,I according to

s,i(t) = (ds,i-t)/ps es es,I (es,k - s,k) 0

Acceptance Test

Documents

Priority Driven Scheduling