real-time systems, dtu, feb 29, 2000 paul pettersson, brics, aalborg, denmark. uppaal’s modeling...

Real-Time Systems, DTU, Feb 29, 2000Paul Pettersson, BRICS, Aalborg, Denmark.

UPPAAL’s Modeling and Specification Language

&Philips Bounded

Retransmission Protocol

Paul PetterssonBRICS@Aalborg


Timed Automata

n

m

a

(Alur & Dill, 1990)

Clocks: x, y

x<=5 & y>3

x := 0

Guard Boolean combination of comp withinteger bounds

ResetAction perfumed on clocks

Transitions

( n , x=2.4 , y=3.1415 ) ( n , x=3.5 , y=4.2415 )

e(1.1)

( n , x=2.4 , y=3.1415 ) ( m , x=0 , y=3.1415 )

a

State ( location , x=v , y=u ) where v,u are in R

Actionused

for synchronization


n

m

a

Clocks: x, y

x<=5 & y>3

x := 0

Transitions

( n , x=2.4 , y=3.1415 ) ( n , x=3.5 , y=4.2415 )

e(1.1)

( n , x=2.4 , y=3.1415 )

e(3.2)

x<=5

y<=10

LocationInvariants

g1g2 g3

g4

Timed Safety Automata = Timed Automata + Invariants

(Henzinger et al, 1992)


Networks of Timed Automata + Integer Variables + arrays ….

l1

l2

a!

x>=2i==3

x := 0i:=i+4

m1

m2

a?

y<=4

…………. Two-way synchronizationon complementary actions.

Closed Systems!


Timed Automata in UPPAAL• Timed (Safety) Automata

+ urgent actions + urgent locations+ committed locations+ data-variables (with bounded domains)+ arrays of data-variables + constants + guards and assignments over data-variables and arrays…+ templates with local clocks, data-variables, and constants.


Declarations in UPPAALclock x1, …, xn;

int i1, …, im;

chan a1, …, ao;

const c1 n1, …, cp np;

Examples:

clock x, y;

int i, J0; int[0,1] k[5];

const delay 5, true 1, false 0;

Array k of five booleans.


Timed Automata in UPPAAL

n

m

a

x<=5 & y>3

x := 0

x<=5

y<=10

g1g2 g3

g4

invinvnxnxinv ,||::

clock natural number and

}!,,,,,{

},,,,{

::

|::

,||::

op

ExpropExprg

nyxnxg

ggggg

d

c

dc

nx :

clock guards

data guards

clock assignments

clock assignments

):?(

|/

|*

|

|

||

|][|::

:

ExprExprg

ExprExpr

ExprExpr

ExprExpr

ExprExpr

Exprn

ExpriiExpr

Expri

d

location invariants


Urgent Channels

urgent chan hurry;

Informal Semantics:• There will be no delay if transition with urgent action can be taken.

Restrictions:• No clock guard allowed on transitions with urgent actions.

• Invariants and data-variable guards are allowed.


Urgent Locations

Click “Urgent” in State Editor.

Informal Semantics:• No delay in urgent location.

Note: the use of urgent locations reduces the number of clocks

in a model, and thus the complexity of the analysis.


Committed Locations

Click “Committed” in State Editor.

Informal Semantics:• No delay in committed location.• Next transition must involve automata in committed location.

Note: the use of committed locations reduces the number of

clocks in a model, and allows for more space and time efficient

analysis.


Philips Bounded Retransmission Protocol

[D’Argenio et.al. 97]


Protocol Overview

• Protocol developed by Philips.

• Transfer data between Audio/Video components via infra-red communication.

• Data files sent in smaller chunks.

• Problem: Unreliable communication medium.

• Sender retransmit if receiver respond too late.

• Receiver abort if sender sends too late.


Overview of BRP

Sender Receiver

S R

K

L

Input: file = p1, …, pn

lossy

lossy

Output: p1, …, pn

BRP

pi

ack


How It Works

• Sender input: file = p1, …, pn.

• S sends (p1,FST,0), (p2,INC,1), …, (pn-1,INC,1), (pn,OK,0).

• R sends: ack, …, ack.

• S retransmits pi if timeout.

• Receiver recives: p1, …, pn.

• Sender and Receiver receives NOK or OK.

whole file OK

more parts

will followfirst part of file


BRP Model Overview

Sender Receiver

S R

K

L

Input: file = p1, …, pn

ack

(pi,INDication,abit)

lossy

lossy

ok, nok, dkIND, ok, nok

Output: p1, …, pn

BRP


The Lossy Media

value-passing

lossy = may drop

messages

one-place

capacity

delay


Bounded Retransmission

• S sends a chunk pi and waits for ack from R.

• If timeout the chunk is retransmitted.

• If too many timeout the transmission fails (NOK is sent to Sender).

• If whole file successfully sent OK is sent to Sender.

• Receiver is similar.


Process S


Process R


The Sender and Receiver

real-time systems, dtu, feb 29, 2000 paul pettersson, brics, aalborg, denmark. uppaal’s modeling...

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