Amo Guangmo Tong - University of Texas at Dallascxl137330/courses/spring14/AdvRTS/... · Amo...

Paper Presentation

Amo Guangmo Tong

University of Taxes at Dallas

[email protected]

February 11, 2014

Amo Guangmo Tong (UTD) February 11, 2014 1 / 26

Overview

1 Techniques for Multiprocessor Global Schedulability Analysis

2 New Response Time Bounds for Fixed Priority MultiprocessorScheduling


Techniques for Multiprocessor Global SchedulabilityAnalysis

Techniques for Multiprocessor Global Schedulability Analysis

Sanjoy Baruah


System Model

Hard real-time system T

n sporadic tasks Tn = (en,Dn, pn)

m identical processors ,m > 1

minimum inter-arrival time or period, pi > 0

execution time ei < pi

relative deadline Di ≤ pi (constrained)

utilization ui = ei/pi


Schedule Algorithms

Partitioned FJP(fixed job priority) algorithmsAssign tasks to processors. Schedule tasks on each uniprocessor.

Example:

Global FJP algorithmsIn this schedule algorithm, tasks can execute and resume on anyprocessors.

Schedulable and Schedulability testAmo Guangmo Tong (UTD) February 11, 2014 5 / 26

Contributions

Global FJP and partitioned FJP are incomparable.

Provide a schedulability test for global EDF.


Global and partitioned FJP scheduling are incomparable.

Step 1

Sometimes global FJP scheduling is better than partitioned FJPscheduling.

Example:

τ1 = (2, 3), τ2 = (3, 4), τ3 = (5, 12); u1 = 2/3, u2 = 3/4, u3 = 5/12.Because u1 + u2 > 1,u2 + u3 > 1,u1 + u3 > 1, partitioned FJP dosenot work.

The following figure shows global FJP works.

1 2 3 4 5 6 7 8 9 10 11 12


Global and partitioned FJP scheduling are incomparable.

Step 2

Sometimes partitioned FJP scheduling is better than global FJPscheduling .Example:

τ1 = (2, 3), τ2 = (3, 4), τ3 = (3, 12), τ4 = (4, 12); u1 = 2/3, u2 =3/4, u3 = 3/12, u4 = 4/12. Because u1 + u4 = 1,u2 + u3 = 1,partitioned FJP works.However no global FJP works. (If we assume τ3,1 has higher prioritythan τ4,1, then τ4,1 misses its deadline.)

1 2 3 4 5 6 7 8 9 10 11 12

Miss deadline


A schedulability test for global EDF

Let focus on τi ,j .

ri ,j = ta, di ,j = td , Di = td − ta, to is the latest time instant before taat which at least one processor is idle.

L: the union of intervals in [ta, td) during which all m processors areexecuting jobs other than τi ,j .

Some proc. Is idle



If τi ,j misses its deadline, then |L| > Di − ei . So there exists anL∗ ⊆ L where |L∗| = Di − ei . And the total execution of all tasksdone in [to , ta)

⋃L∗ is m(Ai + Di − ei ).

Some proc. Is idle



Let I (τk , τi ,Ai ) denote the upper bound of the workload of τk thatcould be done in [to , ta)

⋃L′

where L′

is any subset of [ta, td) withlength Di − ei .I (τk , τi ,Ai ) = I (ek ,Dk ,Ai , ei ,Di )

If, for any value of Ai ,∑n

k=1 I (τk , τi ,Ai ) < m(Ai + Di − ei ), then anyjob τi ,j of τi cannot miss its deadline.

Some proc. Is idle


Test

If for any value A,∑nk=1 I (τk , τ1,A) < m(A + D1 − e1), jobs in τ1 will meet deadline.∑nk=1 I (τk , τ2,A) < m(A + D2 − e2), jobs in τ2 will meet deadline.

.

.

.∑nk=1 I (τk , τn,A) < m(A + Dn − en), jobs in τn will meet deadline.

Thus, if for all i from 1 to n, and any value Ai ,∑nk=1 I (τk , τi ,Ai ) < m(Ai + Di − ei ), then no job in τ will miss deadline.


I (τk , τi)

I (τk , τi ,Ai ) denote the upper bound of the workload of τk that could bedone in [to , ta)

⋃L∗ where L∗ is any subset of [ta, td) with length Di − ei .

I (τk , τi ,Ai ) = I (ek ,Dk ,Ai , ei ,Di )

Some proc. Is idle

Carry in job

No carry in job


Pseudo-polynomial

Previous : O(P(n))

Now:O(P(m, ei , di ))

Other weakness of improvement.


New Response Time Bounds for Fixed PriorityMultiprocessor Scheduling

New Response Time Bounds for Fixed Priority MultiprocessorScheduling

Nan Guan, Martin Stigge, Wang Yi and Ge Yu


System Model

sporadic real-time system T

n sporadic tasks Tn = (en, dn, pn)

m identical processors ,m > 1

minimum inter-arrival time or period, pi > 0

execution time ei < pi

relative deadline Di

Di ≤ pi (constrained-deadline)Di and Pi have no relationship(arbitrary-deadline)

utilization ui = ei/pi

fi ,j denotes the finish time of τi ,j , define response time of τi ,j asfi ,j − ri ,j


Content

Response time bound for constrained-deadline system

Response time bound for arbitrary-deadline system


Constrained-deadline system

To analyze deadline miss

Some proc. Is idle

To analyze response time bound

Some proc. Is idle



When we analyze τi ,j :Let Ωi (x) be the maximum value of the sum of all higher-priority tasks’interference among all possible cases.

Carry-in job

x



Then we solve the equation:

x = bΩi (x)m c+ ei

x

Remember: Ωi(x) be the maximum value of the sum ofall higher-priority tasks’ interference against τi ,j .



Then x is an upper bound of response time of τi ,j

x

Response time


Arbitrary-deadline system

For constrained-deadline system, we analyze :

Some proc. Is idle

For arbitrary-deadline system, we analyze :

x


Arbitrary-deadline system

Similarly, we solve the equation:

x = bΩi (x ,h)m c+ h · ei

x

Remember : Ωi(x , h) be the maximum value of the sumof all higher-priority tasks’ interference against τi ,j .



Then an upper bound of response time of τi ,j is

x − (h − 1) · pi

x

Response time of h jobs


Weakness or improvement


The End


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