Uniprocessor Scheduling

Every Computer will be Embedded Everywhere EVERY COMPUTER WILL BE EMBEDDED EVERYWHERE

Real-Time Systems Design

embedded.seoultech.ac.kr

Seoul National Univ. of Science and Technology Dept. of Electrical and Information Engineering Prof. Choi, Byoung- Wook http:/ / embedded.seoultech.ac.kr @bwchoi2, [e-mail]

EVERY COMPUTER WILL BE EMBEDDED

Uniprocessor Scheduling
Week # 6 embedded.seoultech.ac.kr Every Computer will be Embedded Everywhere

Outline
• • Earliest Deadline First Scheduling Rate-Monotonic Scheduling
– Worst Arrival Phasings – Least Upper Scheduling Bound

•

Summary

3 / 23

Every Computer will be Embedded Everywhere

Dynamic job scheduling
• • Fixed job scheduling
– All jobs that have same tasks have the same fixed priority

Dynamic job scheduling
– Different jobs of the same task cab have different priority

τ1 τ2

4 / 23

Every Computer will be Embedded Everywhere

Earliest Deadline First (EDF) Scheduling
• • Can be used to schedule periodic tasks Uses dynamic priorities and preemptive scheduling
– Higher priority to task with earlier deadline

•

Example: 2- task set where each task is (C, T=D)

{ (2, 4), (3, 7)} 50%

τ1 τ2
43% • Utilization U of task set { ti} for i = 1, …, n:

C Ui = i Ti

5 / 23 i =1

U = ∑U i = ∑

n

Ci i =1 Ti

n

Every Computer will be Embedded Everywhere

EDF Schedulability Condition
Theorem: A task set is schedulable under EDF if and only if U ≤ 1. Proof:

t1
• •

t2

Assume that “ overflow” occurs at time t2. Let t1 be the latest time before t2 such that
– the processor is fully utilized in the interval [ t1 , t2] – only instances with deadlines before t2 executes in [ t1 , t2]

• •

If such a t1 cannot be found, then set t1 = 0. Let Cd be the computational demand in [ t1 , t2] n  t 2 − t1  t 2 − t1 Cd = ∑  * ci = (t 2 − t1 )U  * ci ≤ ∑ Ti  Ti ri ≥ t1 , d1 ≤t 2  i =1

•

But an overflow implies that Cd > ( t2