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Chapter 5: CPU Scheduling Chapter 5: CPU Scheduling

Chapter 5: CPU Scheduling

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Chapter 5: CPU Scheduling. Chapter 5: CPU Scheduling. Basic Concepts Scheduling Criteria Scheduling Algorithms Multiple-Processor Scheduling Real-Time Scheduling Thread Scheduling Operating Systems Examples Java Thread Scheduling Algorithm Evaluation. Levels of Scheduling. Running. - PowerPoint PPT Presentation

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Page 1: Chapter 5:  CPU Scheduling

Chapter 5: CPU SchedulingChapter 5: CPU Scheduling

Page 2: Chapter 5:  CPU Scheduling

5.2 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Chapter 5: CPU SchedulingChapter 5: CPU Scheduling

Basic Concepts

Scheduling Criteria

Scheduling Algorithms

Multiple-Processor Scheduling

Real-Time Scheduling

Thread Scheduling

Operating Systems Examples

Java Thread Scheduling

Algorithm Evaluation

Page 3: Chapter 5:  CPU Scheduling

5.3 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Levels of SchedulingLevels of Scheduling

Running

Ready

Blocked

Blocked,Suspend

Ready,Suspend

New Exit

Short Term

Medium Term

Long Term

Page 4: Chapter 5:  CPU Scheduling

5.4 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Basic ConceptsBasic Concepts

Maximum CPU utilization obtained with multiprogramming

CPU–I/O Burst Cycle – Process execution consists of a cycle of CPU execution and I/O wait

CPU burst distribution

Page 5: Chapter 5:  CPU Scheduling

5.5 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Alternating Sequence of CPU And I/O BurstsAlternating Sequence of CPU And I/O Bursts

Page 6: Chapter 5:  CPU Scheduling

5.6 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Histogram of CPU-burst TimesHistogram of CPU-burst Times

Page 7: Chapter 5:  CPU Scheduling

5.7 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

CPU SchedulerCPU Scheduler

Selects from among the processes in memory that are ready to execute, and allocates the CPU to one of them

CPU scheduling decisions may take place when a process:

1. Switches from running to waiting state

2. Switches from running to ready state

3. Switches from waiting to ready

4. Terminates

Scheduling under 1 and 4 is nonpreemptive

All other scheduling is preemptive

Page 8: Chapter 5:  CPU Scheduling

5.8 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

DispatcherDispatcher

Dispatcher module gives control of the CPU to the process selected by the short-term scheduler; this involves:

switching context

switching to user mode

jumping to the proper location in the user program to restart that program

Dispatch latency – time it takes for the dispatcher to stop one process and start another running

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5.9 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Scheduling CriteriaScheduling Criteria

CPU utilization – keep the CPU as busy as possible

Throughput – # of processes that complete their execution per time unit

Turnaround time – amount of time to execute a particular process

Waiting time – amount of time a process has been waiting in the ready queue

Response time – amount of time it takes from when a request was submitted until the first response is produced, not output (for time-sharing environment)

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5.10 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Optimization CriteriaOptimization Criteria

Max CPU utilization

Max throughput

Min turnaround time

Min waiting time

Min response time

Page 11: Chapter 5:  CPU Scheduling

5.11 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

스케줄링의 기준스케줄링의 기준

고려사항 프로세스의 I/O 위주성 프로세스의 CPU 위주성 뱃치 또는 대화형 실시간성 우선순위 페이지 폴트 빈도 프리엠트된 빈도수 현재까지의 수행시간 완료시까지 추가 수행시간

Page 12: Chapter 5:  CPU Scheduling

5.12 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

스케줄링의 목적스케줄링의 목적

공평할 것 시스템 처리량 최대 적정 응답시간을 받는 이용자수를 극대화 예측 가능할 것 오버헤드를 최소화 균형적 자원 사용 응답성과 이용성의 균형 유지 무한 연기 회피 우선순위를 사용할 것 주요 자원 보유 프로세스에 우선권 부여 거동이 바람직한 프로세스에 좋은 서비스 제공 고도부하시 성능이 점진적으로 저하될 것

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5.13 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

우선순위 우선순위 ((priority)priority)

우선순위 대기 리스트 ( 대기 큐 ) 에서 다음 수행될 Process 를

선택할 때 사용 정적 대 동적 우선순위

정적우선순위 : 우선순위가 한번 부여되면 해당 Process 가 종료될 때까지 불변 장점 : 간단 단점 : 상황변동에 대처 불가

동적우선순위 : 상황 변동에 따라 우선순위값 조정 단점 : Overhead

구입한 우선순위 높은 우선순위를 구입가능

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5.14 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

First-Come, First-Served (FCFS) SchedulingFirst-Come, First-Served (FCFS) Scheduling

Process Burst Time

P1 24

P2 3

P3 3

Suppose that the processes arrive in the order: P1 , P2 , P3

The Gantt Chart for the schedule is:

Waiting time for P1 = 0; P2 = 24; P3 = 27 Average waiting time: (0 + 24 + 27)/3 = 17

P1 P2 P3

24 27 300

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5.15 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

FCFS Scheduling (Cont.)FCFS Scheduling (Cont.)

Suppose that the processes arrive in the order

P2 , P3 , P1

The Gantt chart for the schedule is:

Waiting time for P1 = 6; P2 = 0; P3 = 3

Average waiting time: (6 + 0 + 3)/3 = 3

Much better than previous case

Convoy effect short process behind long process

P1P3P2

63 300

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5.16 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Shortest-Job-First (SJR) SchedulingShortest-Job-First (SJR) Scheduling

Associate with each process the length of its next CPU burst. Use these lengths to schedule the process with the shortest time

Two schemes:

nonpreemptive – once CPU given to the process it cannot be preempted until completes its CPU burst

preemptive – if a new process arrives with CPU burst length less than remaining time of current executing process, preempt. This scheme is know as the Shortest-Remaining-Time-First (SRTF)

SJF is optimal – gives minimum average waiting time for a given set of processes

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5.17 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Process Arrival Time Burst Time

P1 0.0 7

P2 2.0 4

P3 4.0 1

P4 5.0 4

SJF (non-preemptive)

Average waiting time = (0 + 6 + 3 + 7)/4 = 4

Example of Non-Preemptive SJFExample of Non-Preemptive SJF

P1 P3 P2

73 160

P4

8 12

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5.18 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Example of Preemptive SJFExample of Preemptive SJF

Process Arrival Time Burst Time

P1 0.0 7

P2 2.0 4

P3 4.0 1

P4 5.0 4

SJF (preemptive)

Average waiting time = (9 + 1 + 0 +2)/4 = 3

P1 P3P2

42 110

P4

5 7

P2 P1

16

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5.19 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Determining Length of Next CPU BurstDetermining Length of Next CPU Burst

Can only estimate the length

Can be done by using the length of previous CPU bursts, using exponential averaging

:Define 4.

10 , 3.

burst CPU next the for value predicted 2.

burst CPU of lenght actual 1.

1

n

th

n nt

.1 1 nnn t

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5.20 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Prediction of the Length of the Next CPU BurstPrediction of the Length of the Next CPU Burst

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5.21 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Examples of Exponential AveragingExamples of Exponential Averaging

=0 n+1 = n

Recent history does not count =1

n+1 = tn

Only the actual last CPU burst counts If we expand the formula, we get:

n+1 = tn+(1 - ) tn -1 + …

+(1 - )j tn -j + …

+(1 - )n +1 0

Since both and (1 - ) are less than or equal to 1, each successive term has less weight than its predecessor

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5.22 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

SJF(Shortest-Job-First) SJF(Shortest-Job-First) 스케줄링스케줄링((nonpreemptive nonpreemptive 기법기법 ))

Job 의 실행시간이 가장 짧은 작업을 선택 장점 : 평균 대기시간이 짧다 단점 :

시분할 구현이 불가능 Starvation 의 가능성 Job 의 실행시간 예측이 거의 불가능

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5.23 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Priority SchedulingPriority Scheduling

A priority number (integer) is associated with each process

The CPU is allocated to the process with the highest priority (smallest integer highest priority)

Preemptive

nonpreemptive

SJF is a priority scheduling where priority is the predicted next CPU burst time

Problem Starvation – low priority processes may never execute

Solution Aging – as time progresses increase the priority of the process

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5.24 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Round Robin (RR)Round Robin (RR)

Each process gets a small unit of CPU time (time quantum), usually 10-100 milliseconds. After this time has elapsed, the process is preempted and added to the end of the ready queue.

If there are n processes in the ready queue and the time quantum is q, then each process gets 1/n of the CPU time in chunks of at most q time units at once. No process waits more than (n-1)q time units.

Performance

q large FIFO

q small q must be large with respect to context switch, otherwise overhead is too high

Page 25: Chapter 5:  CPU Scheduling

5.25 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Example of RR with Time Quantum = 20Example of RR with Time Quantum = 20

Process Burst Time

P1 53

P2 17

P3 68

P4 24 The Gantt chart is:

Typically, higher average turnaround than SJF, but better response

P1 P2 P3 P4 P1 P3 P4 P1 P3 P3

0 20 37 57 77 97 117 121 134 154 162

Page 26: Chapter 5:  CPU Scheduling

5.26 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Time Quantum and Context Switch TimeTime Quantum and Context Switch Time

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5.27 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Quantum Quantum 의 크기의 크기 길이 고정 대 가변 대단히 클 경우 FIFO 와 동일 작아질수록 문맥교환이 빈번 최적치 : 대부분의 대화형 사용자의 요구가 quantum 보다 짧은

시간에 처리될 경우

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5.28 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Turnaround Time Varies With The Time QuantumTurnaround Time Varies With The Time Quantum

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5.29 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

SRT, HRNSRT, HRN

SRT(Shortest-Remaining-Times First) 스케쥴링 : preemptive

SJF 를 Preemptive 기법으로 변형 대기 list 상의 job 중 남아있는 실행시간 추정치가 가장 작은

작업 선택

HRN(Highest-Response-ratio Next) 스케쥴링 SJF 는 짧은 job 을 지나치게 선호 Nonpreemptive

우선순위 = 대기시간 + 서비스시간

서비스시간

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5.30 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multilevel QueueMultilevel Queue

Ready queue is partitioned into separate queues:foreground (interactive)background (batch)

Each queue has its own scheduling algorithm

foreground – RR

background – FCFS

Scheduling must be done between the queues

Fixed priority scheduling; (i.e., serve all from foreground then from background). Possibility of starvation.

Time slice – each queue gets a certain amount of CPU time which it can schedule amongst its processes; i.e., 80% to foreground in RR

20% to background in FCFS

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5.31 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multilevel Queue SchedulingMultilevel Queue Scheduling

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5.32 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multilevel Feedback QueueMultilevel Feedback Queue

A process can move between the various queues; aging can be implemented this way

Multilevel-feedback-queue scheduler defined by the following parameters:

number of queues

scheduling algorithms for each queue

method used to determine when to upgrade a process

method used to determine when to demote a process

method used to determine which queue a process will enter when that process needs service

Page 33: Chapter 5:  CPU Scheduling

5.33 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Example of Multilevel Feedback QueueExample of Multilevel Feedback Queue

Three queues:

Q0 – RR with time quantum 8 milliseconds

Q1 – RR time quantum 16 milliseconds

Q2 – FCFS

Scheduling

A new job enters queue Q0 which is served FCFS. When it gains CPU, job receives 8 milliseconds. If it does not finish in 8 milliseconds, job is moved to queue Q1.

At Q1 job is again served FCFS and receives 16 additional milliseconds. If it still does not complete, it is preempted and moved to queue Q2.

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5.34 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multilevel Feedback QueuesMultilevel Feedback Queues

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5.35 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multilevel Feedback Queue: PreemptiveMultilevel Feedback Queue: Preemptive

프로세스의 특성에 따라 처리 짧은 작업에 우선권 IO 위주의 작업에 우선권 (IO 장치를 충분히 사용 ) CPU-bound / IO-bound 를 빨리 파악 CPU bound-job : 계산위주의 작업

( 점차 아래로 이동 ) IO bound-job : ( 상위 level 에서 처리 )

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5.36 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Level 1(FIFO)

••• ••• Use theCPU

completion

Level 2(FIFO)

••• ••• Use theCPU

completion

Level 3(FIFO)

••• ••• Use theCPU

completion

Level n(round robin)

••• ••• Use theCPU

completion•••

preemption

preemption

preemption

preemption

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5.37 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

100 percent

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Page 38: Chapter 5:  CPU Scheduling

5.38 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

100 percent

SYSTEMRESOURCES

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Page 39: Chapter 5:  CPU Scheduling

5.39 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Multiple-Processor SchedulingMultiple-Processor Scheduling

CPU scheduling more complex when multiple CPUs are available

Homogeneous processors within a multiprocessor

Load sharing

Asymmetric multiprocessing – only one processor accesses the system data structures, alleviating the need for data sharing

Symmetric multiprocessing – each processor is self-scheduling

processor afinity

Page 40: Chapter 5:  CPU Scheduling

5.40 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

5. 8 5. 8 Typical SMT architectureTypical SMT architecture

SMT : Symmetric multithreadingSMT : Symmetric multithreading - provide multiple logical- rather than physical- - provide multiple logical- rather than physical- processors processors

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5.41 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Real-Time SchedulingReal-Time Scheduling

Hard real-time systems – required to complete a critical task within a guaranteed amount of time

Soft real-time computing – requires that critical processes receive priority over less fortunate ones

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5.42 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Dispatch LatencyDispatch Latency

Page 43: Chapter 5:  CPU Scheduling

5.43 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Deadline Deadline 스케쥴링 스케쥴링 (( 기한부 스케쥴링기한부 스케쥴링 ))

각 job 이 마감시간을 가짐 각 job 이 마감시간내에 처리되도록 스케쥴 문제점 : 구현이 거의 불가능

Deadline 을 사용자가 예측 불가능 일부 사용자 희생 Overhead 가 큼

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5.44 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Priority Inversion #1Priority Inversion #1

Thread A(high priority)

Thread B(low priority)

unlock mlock m

Time

blocked Running ready

scheduled lock m

Priority inversion

Page 45: Chapter 5:  CPU Scheduling

5.45 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Priority Inversion #2Priority Inversion #2

Thread A(high priority)

Thread C(low priority)

lock m

Time

blocked running ready

scheduled lock m

Priority inversion

Thread B(medium priority)

scheduled

Page 46: Chapter 5:  CPU Scheduling

5.46 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Priority Inheritance ProtocolPriority Inheritance Protocol

Thread A(priority p+x)

Thread B(priority p)

unlock mlower to plock m

Time

blocked running ready

scheduled lock m

raise top+x

Page 47: Chapter 5:  CPU Scheduling

5.47 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Priority Ceiling ProtocolPriority Ceiling Protocol

Thread A(priority p+x)

Thread B(priority p)

unlock mlower to p

Time

blocked running ready

scheduled lock m

lock mraise to p+x

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5.48 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Thread SchedulingThread Scheduling

Local Scheduling – How the threads library decides which thread to put onto an available LWP

Global Scheduling – How the kernel decides which kernel thread to run next

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5.49 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Pthread Scheduling APIPthread Scheduling API

#include <pthread.h>#include <stdio.h>#define NUM THREADS 5int main(int argc, char *argv[]){

int i;pthread t tid[NUM THREADS];pthread attr t attr;/* get the default attributes */pthread attr init(&attr);/* set the scheduling algorithm to PROCESS or SYSTEM */pthread attr setscope(&attr, PTHREAD SCOPE SYSTEM);/* set the scheduling policy - FIFO, RT, or OTHER */pthread attr setschedpolicy(&attr, SCHED OTHER);/* create the threads */for (i = 0; i < NUM THREADS; i++)

pthread create(&tid[i],&attr,runner,NULL);

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5.50 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Pthread Scheduling APIPthread Scheduling API

/* now join on each thread */

for (i = 0; i < NUM THREADS; i++)

pthread join(tid[i], NULL);

}

/* Each thread will begin control in this function */

void *runner(void *param)

{

printf("I am a thread\n");

pthread exit(0);

}

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5.51 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Java Thread SchedulingJava Thread Scheduling

JVM Uses a Preemptive, Priority-Based Scheduling Algorithm

FIFO Queue is Used if There Are Multiple Threads With the Same Priority

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5.52 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Java Thread Scheduling (cont)Java Thread Scheduling (cont)

JVM Schedules a Thread to Run When:

1. The Currently Running Thread Exits the Runnable State

2. A Higher Priority Thread Enters the Runnable State

* Note – the JVM Does Not Specify Whether Threads are Time-Sliced or Not

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5.53 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Time-SlicingTime-Slicing

Since the JVM Doesn’t Ensure Time-Slicing, the yield() Method

May Be Used:

while (true) {

// perform CPU-intensive task

. . .

Thread.yield();

}

This Yields Control to Another Thread of Equal Priority

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5.54 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Thread PrioritiesThread Priorities

Priority Comment

Thread.MIN_PRIORITY Minimum Thread Priority

Thread.MAX_PRIORITY Maximum Thread Priority

Thread.NORM_PRIORITY Default Thread Priority

Priorities May Be Set Using setPriority() method:

setPriority(Thread.NORM_PRIORITY + 2);

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5.55 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Scheduler - TPScheduler - TP/** * Scheduler.java

*/

public class Scheduler extends Thread

{

private CircularList queue;

private int timeSlice;

private static final int DEFAULT_TIME_SLICE = 1000; // 1 초

public Scheduler() {

timeSlice = DEFAULT_TIME_SLICE;

queue = new CircularList();

}

public Scheduler(int quantum) {

timeSlice = quantum;

queue = new CircularList();

}

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5.56 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Scheduler - TPScheduler - TP // adds a thread to the queue

public void addThread(Thread t) {

t.setPriority(2);

queue.addItem(t);

}

// this method puts the scheduler to sleep for a time quantum

private void schedulerSleep() {

try {

Thread.sleep(timeSlice);

} catch (InterruptedException e)

{};

}

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5.57 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Scheduler - TPScheduler - TP public void run() {

Thread current;

// set the priority of the scheduler to the highest priority

this.setPriority(6);

while (true) {

current = (Thread)queue.getNext();

if ( (current != null) &&

(current.isAlive()) {

current.setPriority(4);

schedulerSleep();

current.setPriority(2);

}

}

}

}

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5.58 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

/**

* TestScheduler.java

* This program demonstrates how the scheduler operates.

* This creates the scheduler and then the three example threads.

*/

public class TestScheduler

{

public static void main(String args[]) {

/**

* This must run at the highest priority

* to ensure that it can create the scheduler and the example

* threads. If it did not run at the highest priority, it is

* possible that the scheduler could preemt this and not allow

* it to create the example threads.

*/

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5.59 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Thread.currentThread().setPriority(Thread.MAX_PRIORITY);

scheduler CPUScheduler = new scheduler();

CPUScheduler.start();

TestThread t1 = new TestThread("Thread 1");

t1.start();

CPUScheduler.addThread(t1);

TestThread t2 = new TestThread("Thread 2");

t2.start();

CPUScheduler.addThread(t2);

TestThread t3 = new TestThread("Thread 3");

t3.start();

CPUScheduler.addThread(t3);

}

}

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5.60 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Operating System ExamplesOperating System Examples

Solaris scheduling

Windows XP scheduling

Linux scheduling

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5.61 Silberschatz, Galvin and Gagne ©2005Operating System Concepts

Solaris 2 SchedulingSolaris 2 Scheduling

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Solaris Dispatch Table Solaris Dispatch Table

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Windows XP PrioritiesWindows XP Priorities

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Linux SchedulingLinux Scheduling

Two algorithms: time-sharing and real-time Time-sharing

Prioritized credit-based – process with most credits is scheduled next

Credit subtracted when timer interrupt occurs When credit = 0, another process chosen When all processes have credit = 0, recrediting occurs

Based on factors including priority and history Real-time

Soft real-time Posix.1b compliant – two classes

FCFS and RR Highest priority process always runs first

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The Relationship Between Priorities and Time-slice lengthThe Relationship Between Priorities and Time-slice length

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List of Tasks Indexed According to ProritiesList of Tasks Indexed According to Prorities

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Algorithm EvaluationAlgorithm Evaluation

Deterministic modeling – takes a particular predetermined workload and defines the performance of each algorithm for that workload

Queueing models

Implementation

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Deterministic modelingDeterministic modeling

Process Burst Time

P1 10

P2 29

P3 3

P4 7

P5 12

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FCFSFCFS

Average waiting time = 28

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SJF(nonpreemptive)SJF(nonpreemptive)

Average waiting time = 13

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RRRR

Average waiting time = 23

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큐잉 모델큐잉 모델 개요

큐잉 이론과 마코프 프로세스 시스템의 행태를 수학적으로 표현한 것

큐잉 이론 큐잉 이론 : theory of waiting lines 서비스 용량 (money) 대 대기열 (time)

Server 1

Server 2

Server C

Service facility with identical servers

Queue or waiting line of customers

Input traffic

Population of customers

•••

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큐잉 모델큐잉 모델 Unbounded vs. bounded queue

다수의 random variable 사용

• q: waiting time• s: service time• w: 큐잉 시스템내 체류시간• w = q + s

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큐잉 모델큐잉 모델

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트래픽 밀도트래픽 밀도

트래픽 밀도 u : 손님을 효율적으로 서비스하는 능력의 측정치

트래픽 밀도 : 최소 서버수의 결정에 사용 예 ,

따라서 4 명의 서버가 필요

서비스율 : 도착율 ,:

)()()(

SE

ESE

u

43 ,5)( ,17)( .uESE

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5.15 5.15 Evaluation by simulationEvaluation by simulation

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End of Chapter 5End of Chapter 5