Lecture07-aperiodic

8/3/2019 Lecture07-aperiodic

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Priority-driven Scheduling of Aperiodic and

Sporadic Tasks (2)

Advanced Operating Systems (M)Lecture 7


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Scheduling aperiodic jobs (contd) Sporadic servers Constant utilisation servers Total bandwidth servers

Weighted fair queuing servers

Scheduling sporadic jobs

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Lecture Outline


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Limitation of deferrable servers they may delaylower-priority tasks for more time than a periodictask with the same period and execution time:

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Limitations of Deferrable Servers

0 1 2 3 4 5 6 7 8 9

T2=(p=6.5, e=0.5)

T1=(=2,p=3.5, e=1.5)

TDS=(p=3, e=1)

0

1Budget

JA released

Budget replenished

Budget exhausted

Budget replenished

T1 blocked for 1.2 units although execution

time of deferrable server is only 1.0 units


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Sporadic Servers

A sporadic server is designed to eliminate thislimitation

A different type of bandwidth preserving server: several different sub-types

More complex consumption and replenishment rules ensure that asporadic server with periodpS and budget eSnever demands moreprocessor time than a periodic task with the same parameters


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System, T, of independent preemptable periodictasks and a sporadic server with parameters (ps, es)

Fixed-priority scheduling; system can be scheduled if sporadic serverbehaves as a periodic task with parameters (ps, es)

Define: TH : the periodic tasks with higher priority than the server (may be empty) tr : the last time the server budget replenished tf : the first instant aftertrat which the server begins to execute

At any time tdefine: BEGINas the start of the earliest busy interval in the most recent contiguous sequence of

busy intervals ofTHstarting before t(busy intervals are contiguous if the later one startsimmediately the earlier one ends)

END as the end of the latest busy interval in this sequence if this interval ends before t;defineEND = if the interval ends aftert

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Simple Fixed-Priority Sporadic Server


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Consumption rule: At any time ttr, if the server has budget and if either of the following two

conditions is true, the budget is consumed at the rate of 1 per unit time:

C1: The server is executing C2: The server has executed since trandEND < t

When they are not true, the server holds its budget

That is:

The server executes for no more time than it has execution budget

The server retains its budget if: A higher-priority job is executing, or It has not executed since tr

Otherwise, the budget decreases when the server executes, or if it idleswhile it has budget

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Replenishment rules R1: When system begins executing, and each time budget is replenished,

set the budget to eS and tr= the current time.

R2: When server begins to execute (defined as time tf)ifEND = tf then

te = max(tr,BEGIN)

else ifEND < tf thente = tf

The next replenishment time is set to te +pS

R3: budget replenished at the next replenishment time, unless:

Ifte +pS is earlier than tf the budget is replenished as soon as it is exhausted

IfTbecomes idle before te + pS, and becomes busy again at tb, the budget is replenished atmin(tb, te +pS)

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te = effective replenishment time


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Example: Fixed-Priority Sporadic Server

TSS

T1

T2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

T3

T1=(3, 0.5), T2=(4, 1.0), T3=(19, 4.5), Tss=(5, 1.5)

Rate monotonic schedule; simple sporadic server

A1: r = 3, e = 1

A2: r = 7, e = 2

A3: r = 15.5, e = 2

A1 A2 A3

Max. blocking time due

to sporadic server = 1.5


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Example: Fixed-Priority Sporadic Server

90.0

1.0

Budget

0.5

1.5

No aperiodic jobs

server suspended

JobA1 released,

server blocked

JobA1 executes

Budget continues to be usedaccording to rule C2

JobA2 released

but no budget

Budget availablebut blocked

JobA2 executes

No budget

Sporadic server is constrained to executefor at most 1.5 units out of every 5, due toconsumption and replenishment rules

A1 A2 A3

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TSS

T1

T2


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More complex than a polling server or a deferrableserver, but much easier to prove the system can bescheduled

Theorem: for the purpose of validating a schedule,you can treat a simple sporadic server(ps, es) in a

fixed-priority system exactly the same as any other

periodic task Ti withpi=ps and ei = es The actual inter-release times of the sporadic server will sometimes be

greater thanps, and their execution times less than es, but this does notaffect correctness

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It is possible to define a simple sporadic server tooperate in a dynamic-priority environment

E.g., when using EDF or LST scheduling

Consumption and replenishment rules conceptuallysimilar to those for a fixed-priority scheduler, withminor modifications that account for the differencein scheduling algorithm

Provides same scheduling guarantees as the simple sporadic server for

fixed-priority schedulers

A simple sporadic server(ps, es) in an EDF or LST system can be treatedexactly the same as any other task Ti withpi =ps and ei = es when testingwhether the system can be scheduled

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Simple Dynamic-Priority Sporadic Server


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Two other bandwidth preserving server algorithmsoften used for process scheduling:

Constant utilisation server Total bandwidth server

Used in virtual machine systems, to assign knownfraction of processor time to some task

Aiming to provide fair sharing, timing isolation, or guaranteed throughput

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Other Bandwidth Preserving Servers


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Constant utilisation server reserves a fraction, s, ofthe processor time for execution of the server

Like other bandwidth preserving servers, it has abudget and is defined in terms of consumption andreplenishment rules

When the budget is non-zero, the server isscheduled with other tasks on an EDF basis

The budget and deadline of the server are chosen such that the utilisationof the server is constant when it executes, and that it is always givenenough budget to complete the job at the head of its queue each time itsbudget is replenished

The server never has any budget if it has no work to do

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Constant Utilisation Server


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Consumption rule: A constant utilisation server only consumes budget when it executes

Replenishment rules:

Initially, budget es = 0 and deadline d= 0 When an aperiodic job with execution time e arrives at time tto an emptyaperiodic job queue

Ift < d, do nothing ( server is busy; wait for it to become idle)

Iftdthen set d = t + e/s and es = e

At the deadline d of the server If the server is backlogged, set d = d + e/s and es = e ( was busy when job arrived) If the server is idle, do nothing

i.e., the server is always given enough budget to complete the job at thehead of its queue, with known utilisation, when the budget is replenished

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Constant Utilisation Server


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A total bandwidth server improves responsivenessby allowing a server to claim background time notused by the periodic tasks

Change the replenishment rules slightly, leave all else the same: Initially, es = 0 and d= 0 When an aperiodic job with execution time e arrives at time tto an empty aperiodic job queue,

set d= max(d, t) + e/s and es = e

When the server completes the current aperiodic job, the job is removed from the queue and,if the server is backlogged, set d = d + e/s and es = e; if the server is idle, do nothing

Always ready for execution when backlogged

Assigns at least fraction s of the processor to a task

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Total Bandwidth Server


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Consider the problem of scheduling sporadic jobsalongside a system of periodic tasks and aperiodicjobs

Recall the sporadic job scheduling problem: Based on the execution time and deadline of each newly arrived sporadic

job, decide whether to accept or reject the job

Accepting the job implies that the job will complete within its deadline,without causing any periodic task or previously accepted sporadic job tomiss its deadline

Do not accept a sporadic job if cannot guarantee it will meet its deadline

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Scheduling Sporadic Jobs


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When sporadic jobs arrive, they are both acceptedand scheduled in EDF order

In a dynamic-priority system, this is the natural order of execution In a fixed-priority system, the sporadic jobs are executed by a bandwidth

preserving server, which performs an acceptance test and runs thesporadic jobs in EDF order

In both cases, no new scheduling algorithm is required

Definitions:

Sporadic jobs are denoted by Si(ri, di, ei) where ri is the release time, di isthe (absolute) deadline, and ei is the maximum execution time

The density of a sporadic job i = ei/(diri) The total density of a system of n jobs is =1 +2 + +n

The job is active during its feasible interval (ri, di]

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Model for Scheduling Sporadic Jobs


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Theorem: A system of independent preemptablesporadic jobs can be scheduled using EDF if thetotal density ofallactive jobs in the system 1 atall times

This is the standard scheduling test for EDF systems, but including bothperiodic and sporadic jobs

This test uses the density since deadlines may not equal periods; hence itis a sufficient test, but not a necessary test

What does this mean?

If we can bound the frequency with which sporadic jobs appear to therunning system, we can guarantee that none are missed

Alternatively, when a sporadic job arrives, if we deduce that the totaldensity would exceed 1 in its feasible interval, we reject the sporadic

job (admission control)

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Sporadic Jobs in Dynamic-Priority Systems


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At time tthere are n active sporadic jobs, stored innon-decreasing order of deadline

The deadlines partition the time from tto into n + 1 discrete intervals:I1,I2, ,In+1

I1 begins at tand ends at the earliest sporadic job deadline

For each 1 kn, each intervalIk+1 begins when the intervalIkends, and ends at the nextdeadline in the list (or forIn+1)

The scheduler maintains the total density s,kof each intervalIk

LetIlbe the interval containing the deadline dofthe new sporadic job S(t, d, e) The scheduler accepts the job if

for all k= 1, 2, , l

i.e. accept if the new sporadic job can be added, without increasing thedensity of any intervals past 1

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Admission Control for Sporadic Jobs/EDF

Density of new jobe

d t+s,k 1


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Notes: This acceptance test is notoptimal: a sporadic job may be rejected even

though it could be scheduled (the result for the schedulable utilisation isbased on the densityand hence is sufficient but not necessary)

It is possible to derive a much more complex expression taking intoaccount slack time, that is optimal. Unclear if the complexity is worthwhile.

This acceptance test assumes every sporadic job is ready for executionwhen released

If this is not the case, must modify the acceptance test to take into account the time when thejobs become ready, rather than their release time, when testing the intervals to see if theirdensity exceeds 1

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Admission Control for Sporadic Jobs/EDF


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Use a sporadic server to execute sporadic jobs in afixed-priority system

The server(ps, es) has budget es units everyps units of time, so thescheduler can compute the least amount of time available to everysporadic job in the system

Assume that sporadic jobs ordered among themselves in EDF When first sporadic job S1(t, ds,1, es,1) arrives, there is at least

(ds,1t)/pses units of processor time available to the serverbefore the deadline of the job

(ds,1t)/ps = number of server periods available

Therefore it accepts S1 if slack of job

[contd]21

Sporadic Jobs in Fixed-Priority Systems

Time available

Execution time

s,1(t) = b(ds,1 t)/psc es es,1 0


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To decide if a new job Si(t, ds,i, es,i) is acceptable when there are n sporadicjobs in the system, the scheduler first computes the slack s,i(t) ofSi:

where s,k is the execution time of the completed part of the existing job Sk

The job cannot be accepted ifs,i(t) < 0 As fors,1(t), but accounting for the already accepted sporadic jobs

Ifs,i(t) 0, the scheduler then checks if any existing sporadic job Skwithdeadline afterds,i may be adversely affected by the acceptance ofSi

Check if the slack s,k(t) for each Skat the time is at least equal to the execution time es,i ofSi(i.e., Si is accepted ifs,k(t) es,i 0 for every existing sporadic job Skwith deadline ds,i)

This acceptance test for fixed-priority systems is more complex than thatfor dynamic-priority systems, but is still of reasonable time complexity tobe implemented on-line

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Sporadic Jobs in Fixed-Priority Systems

s,i(t) = b(ds,i t)/psc es es,i X

ds,k


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POSIX Scheduling API: Sporadic Server

Hybrid sporadic/background server included in realtime extensions to POSIX Use the SCHED_SPORADIC scheduling policy

When server has budget, runs at sched_priority, otherwise runs as abackground server at sched_ss_low_priority

Set sched_ss_low_priority to be lower priority than real-time tasks, but possibly higher thanother non-real-time tasks in the system

Also defines the replenishment period and the initial budget afterreplenishment

As usual with POSIX, applicable to fixed-priority systems only

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struct sched_param {

int sched_priority;int sched_ss_low_priority;struct timespec sched_ss_repl_period;struct timespec sched_ss_init_budget;

};


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Have discussed further: Scheduling aperiodic jobs (contd)

Sporadic servers Constant utilisation servers Total bandwidth servers

Weighted fair queuing servers

Scheduling sporadic jobs

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Summary

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