Analysis of Real-Time Scheduling Problems in Time PEtri Net Models

8/12/2019 Analysis of Real-Time Scheduling Problems in Time PEtri Net Models

1/34

Analysis of Real-Time SchedulingProblems by Single Step and

Maximal Step Semantics for TimePetri Net Models

Romulo Freitas 1, Raimundo Barreto 1 andPaulo Maciel 2

1Institute of Computing - UFAM2Center of Informatics - UFPE


2/34

Big Picture


3/34


4/34

Introduction

Real-time systems c!eduling

"P-#ard Runtime Pre-runtime

$ime Petri nets Analysis

ingle tep Ma%imal tep


5/34

hy Pre-runtime!

R"NTIM# Priority-dri&en Adapta'le May pro&ide poor results (!en considering

inter-tas)s relationsPR#-R"NTIM#

"on priority-dri&en Infle%i'le It !as good results (!en considering inter-

tas)s relations


6/34

6

hy Pre-runtime!

$as) Release Computation *eadline

A + + +. 2+ 2+ 1

C /+ + 0+

$% cannot preempt B&

Priority E*F

2

1

Periodic $as)s


7/34


8/34


9/34


10/34

Time Petri Net

A time Petri net $P" is a 'ipartitedirected grap! represented 'y a tuple

P 5 Places$ 5 $ransitions

F 5 Flo( relation arcs6 5 6eig!t of t!e arcsm

+ 5 Initial mar)ings

I 5 $iming inter&al


11/34

Time Petri Net


12/34

Single and Maximal Step

ingle step semantics means 7firingone transition at a time8

Ma%imal step semantics means 7firingall concurrent non conflictingtransitions at t!e same time8


13/34

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

M2 M

M/




14/34

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

t+

M2 M

M/

s+5:t+;




15/34

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

t+

M2 M

M/

s+5:t+;



t1


16/34

t1

t2

t1

t2

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

t+

M2 M

M/

s+5:t+;s+5:t+;




17/34

t1

t2

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

t+

M2 M

M/

s+5:t+;s+5:t+;

s15:t1,t2;




18/34

t1 t2

t2 t1

t

p+

t+

p2t2

p/

tp9

p1

t1

p

M+

M1

M9

M+

M1

M2

M

t+

M2 M

M/

s+5:t+;

s15:t1,t2;

s25:t ;




19/34


t+

p+

MSS / 55t'6 t(76 5t.77

p1

t1 t2


20/34

Modeling%omposition of Building Bloc8s


21/34


22/34

Modeling#xclusion Relation


23/34

ModelingInterprocessor %ommunication


24/34

Analysis of the Modelsingle (S, MF){ if (S.M = MF) return TRUE; tag (S); PT = firable (S);

if (|PT| = 0) return FA SE; f!r ea"# ($t, t#eta% in PT) { S& = fire (S, t, t#eta); if (untag(S&) ' single (S&, MF)) { a in T TS (S, S&, t, teta);

return TRUE; * * return FA SE;*


25/34

Analysis of the Model +a i+al (S, MF)

{ if (S.M = MF) return TRUE; tag(S); MSS = +a i+al ste- (firable(S));

if (|MSS| = 0) return FA SE; f!r ea"# (MS in MSS) { f!r ea"# (t#eta in F (MS) { S&= fire(S, MS, t#eta); if (untag(S&) ' +a i+al (S&, MF)) {

a in trans s/ste+ (S, S&, MS, t#eta); return TRUE; * * * return FA SE;*


26/34

# i t 9


27/34

#xperiments 9.

excitation

ac:uisition

control

communication


28/34

#xperiments 9.

;.' PR#%#N2#N%# relations

$E1 PRECE*E $E2 $E2 PRECE*E $E

$E PRECE*E $E/ $A1 PRECE*E $A2

$A2 PRECE*E $A $A PRECE*E $A/

$A/ PRECE*E $A9 $A9 PRECE*E $Aufam>edu>br

Documents

Analysis of Real-Time Scheduling Problems in Time PEtri Net Models