Operating System Concepts and Techniques Lecture 6

Scheduling-2*

M. Naghibzadeh

ReferenceM. Naghibzadeh, Operating System Concepts and Techniques, First ed., iUniverse Inc., 2011.

To order: www.iUniverse.com, www.barnesandnoble.com, or www.amazon.com

* if your time table does not allow to cover all lectures, you can skip this lecture.

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Analytical approach to schedulingModelling is one scientific approach to

analytical investigationsThe following is a simple model of a

uniprocessor multiuser computing systemIt is based on queuing methodology

User 1

User 2

User n

Processor

Interarrival distributionArrival and service patterns are often assumed

to obey Poisson distributionIt can be shown that if the following two

conditions satisfy the interarrival distribution is Poisson distribution

1. Arrival of new requests is independent of the history of the system and the current status of the

queue2. We can always define a time interval dt so small

that the probability of more than one arrival within any period (t, t+dt) is negligible. The probability of

one arrival in such an interval is equal to dt. Here, is a constant which is called arrival rate

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Interarrival distribution…To show, let P0(t) represent the probability that there is no

arrival within the interval (0, t), then P0(t+dt) = Pr [ N(0, t+dt ) = 0]

= Pr [ N(0,t) = 0 AND N(t, t+dt) = 0].From Assumption 1, Pr [ N(0,t) = 0 AND N(t, t+dt) = 0]

= Pr [ N(0,t)=0] Pr [ N(t, t+dt) = 0] = P0(t) (1- dt).

Therefore, P0(t+dt) = P0(t) (1- dt)Or (6.3)

The left side of equation (6.3) is the definition of the derivative when dt approaches zero, thus:

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)()()(

000 tP

dttPdttP

)()(

0

0

tPtp

Interarrival distribution…Or, from differential equations (6.4)

But P0(0) = 1 , replacing t by zero in (6.4), we get:

Which leads to c = 0, hence

Or

Or F(t) = 1 – P0(t) = 1 – probability density function (pdf) of the above distribution is:

t >0, > 0 (6.6)

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cttPn )(0cPn 0)0(0

ttPn )(0tetP )(0

te

tetFtf )()(

Interarrival distribution…The expected value is

Hence, inter-arrival time is exponential and we expect to receive a new arrival every time

Following a similar discussion shows the system completes serving a request every time

This argument shows there are highly analytical arguments concerning many aspects of

operating system

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1)()(

0

dttfttE

1

1

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Multiprocessor schedulingProcessor types

Symmetric Multi-Processor (SMP); homogeneous system asymmetric multiprocessor; heterogeneous system

Processor Affinity hard affinity soft affinity

Synchronization Frequency Independent parallelism Coarse-grain parallelism

Fine-grain parallelismAssignment

static dynamic

Multiprocessor schedulersFirst-Come-First-Served

Shortest Job NextShortest Remaining Time Next

Fair-Share SchedulingRound Robin

Gang Scheduling, i.e., coscheduling

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SMP Process Scheduling in Linux

For Symmetric Multi-Processor (SMP) Usually assign the processor which was used

last time There are preemptable and non-

preemptable processes Preempt if higher priority and hardware

cache rewrite time is less than time quantum

Respect processor affinty Uses SCHED_FIFO, SCHED_RR,

SCHED_OTHER

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Real-time schedulinghard real-time system

Do it in time or catastrophesoft real-time system

No catastrophe but inaccuracyRequest period

Periodic Apriodic Spradic

Most common hard real-times are periodic

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Rate Monotonic (RM)Periodic tasksStatic priority

A task with higher request rate, i.e., a shorter request interval, is assigned a

higher prioritySafety verification

Safe if Ulub = n (21/n –1). Where U=

Optimal static priority for single processors

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n

1iii r/e

Earliest Deadline First (EDF)

Periodic tasksDynamic priority

Works like this: If the system has just started, picks the request

with the closest deadline The execution of a request is completed, a request with the closest deadline from ready queue is picked If the processor is running a process and a new

request with a closer deadline arrives, Process switching takes place

Optimal dynamic priority for single processor

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Least Laxity First (LLF)Periodic tasks

Dynamic priorityWorks like this:

The laxity of a request at any given moment is the time span that it can tolerate before which time it has to be picked up for execution, i.e., L = D – T -

(E-C)Always run a task with least laxity

Disadvantage: for two processes with the equal and least, the processor has to continuously

switch between these two processes, UnpracticalOptimal dynamic priority

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SummaryA scheduling strategy is usually designed to attain

a defined objective, although multi-objective strategies are also possible

Average turnaround time (ATT) may be used to estimate the expected time length in which a

request is completed after being submitted to the system. This could be a good measure of

performanceBased on ATT different scheduling algorithms were

investigatedBesides, in this chapter, I/O scheduling was studied

and different schedulers such as FIFO, LIFO, SSTF, Scan, and C-Scan were introduced

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Find outIn a single-processor multi-programming How

average response time is computedHow many symmetric processors your laptop

supportsReasons behind processor affinity

Sample fine-grain parallelism applicationsReasons behind gang scheduling

Actual hard and soft real-time applicationsDisadvantages of earliest deadline first scheduling

strategySystems which are not safe under RM but are safe

under relative urgency (RU)

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Any questions?