Modelado de Sistemas con Redes de Petri 3-LNS...2 Resumen La finalidad de esta presentación es...

Modelado de Sistemas con Redes de Petri 3-LNS

Dr. Emmanuel López-NeriCentro de Investigación, Innovación y Desarrollo

Tecnológico

2

Resumen

La finalidad de esta presentación es proporcionar los fundamentos de las redes de Petri de tres niveles para su aplicación al modelado y análisis de sistemas de eventos discretos.

Se presentan los conceptos básicos de modelado.

Contenido

1. Sistemas de Eventos Discretos

2. Redes de Petri

3. Modelado de Sistemas

4. Extensiones PN (3-LNS)

5. Tráfico Urbano Modelado con 3-LNS

6. Sistemas Multi-agentes modelado con 3-LNS

4

1.1 Discrete event systems (DES)

The behavior is characterized by a sequence finite or infinite of states delimited by asynchronous events

Almost all DES are man made:-computer systems (operating, communication, data processing systems)-discrete production systems (manufacturing systems)

Some continuous systems can be dealt as DES if it is considered as events,-thresholds of continuous variables-the beginning and ending of the subsystem operation

Time

States

X1

X2

X3

X4

X5

X6

5

1.2 Modeling Formalisms

Importance of modeling

System development life cycle

MODEL VALIDATION

- Simulation- Formal tests(verification ofproperties

Adjustments

Requirements

SYSTEM

description(modeling)

implementation

6

Modeling formalismsCommon language

• Allows communication• Avoids ambiguities

Welcomed features Clearness Ability to describe

- States - Resource management- Events - Concurrency- Synchronization - Cyclic behavior- Decision

Compactness Simple mathematical support Analysis techniques

7

2 Petri net Basics

2.1 Net systems2.2 Modeling examples2.3 Properties of PN2.4 Analysis techniques

8

2.1 Net Systems2.1.1 THE NOTION OF PETRI NETS (PN)

A Petri net consists of :

- A net structure: a bipartite digraph

- A state description:the marking

- A transition rule: the token game

9

Components

PN structureBipartite digraph:Two kind of vertex:

- places: circles- transitions: bars or rectangles

(Weighted) directed arcs: (labeled) arrows

t5

p1 p2 p3

p4 p5 p6

t1

t2

t4

t3

10

Components

PN markingDistribution of marks or tokens (dots) into the places (notion of state in finite state machines)

- Initial marking: initial token allocation

Input/Output Places. The places whose arcs lead to (issue from) atransition tj are called input (output) places of tj.Notation. input places tj ,output places tj

pi

11

Components

Token evolution a two-part transition firing rule:- Enabled transition:

the input places must have at least as many tokens as the weight of the input arcs

- Transition firing: a) remove tokens of the input places (indicated by the weight of

the input arcs)b) add tokens to the output places (indicated by the weight of the output arcs)

2

t

12

Components

Token evolution a two-part transition rule:- Enabled transition:

the input places must have at least as many tokens as the weight of the input arcs

- Transition firing: a) remove tokens of the input places (indicated by the weight of

the input arcs)b) add tokens to the output places (indicated by the weight of the output arcs)

2

t

13

2.2 Modeling examples

2.2.1 INTERPRETED PETRI NETS (IPN)

Interpretation: to give a meaning to the elements of a

PN according to a given context.

- Places: resources, operations, partial states, buffers, mailboxes, ...

- Transitions: events, activities, conditions, ...

- Tokens: commands, parts, messages, ...

14

INTERPRETED PETRI NETS

Interpreted PN: associates

- inputs to the transitions

- outputs to the places

SYSTEM

Inputs

Output

s

15

2.2.2 INTRODUCTORY EXAMPLES

Two synchronized processes

Sequence:- The cars start (authorized by M)

simultaneously to the right;

- when end position is reached

the cars inverse its motion.

- When the initial position is

detected, every car stops.

- A new cycle starts when both

cars are stopped

abcdM

L1R1

L2R2

16

Two synchronized processes

t5

p1 p2 p3

p4 p5 p6

t1

t2

t4

t3R1

R2

L1

L2

M

ab

d c

17

Three processes

Sequence-Cars 1 and 2: the first one arriving to the right position waits to the other one to start the return together

-Car 3: independent cycle

M

I1 D1

a b1

I2 D2

c d2

I3 D3

e f3

M

D1 D2 D3

b d f

I1 I2 I3

a c e

18

State machine

D1,D2,D3 D1,D3

D1,D2,I3

D2,D3

b

d

f

I1,I2,D3

D2,I3

D1,I3

D1,D2e

d

f

b

d

a

I2,D3

I1,D3

I1,I2,I3

I1,I2

D2

D1

f

c

d

eb

e

b

d

d

b

I1,I3

I2,I3

D3c

f

a

f

Ma

c

e

1 2 1

2

I3

I1

I2

e.M

c.M

a.M

f

c

a

e

c

a

e.M

c.M

a.M

b

cm,a,c,e

f

f

f

d,b

b,d,f,

b,d

19

3 Modeling of Systems

3.1 Examples of DES models3.2 Modeling techniques

Curso COSNET 2002ESPECIFICACION Y ANALISIS FORMALES

DE SISTEMAS CON REDES DE PETRI

20

3.1 Examples of DES models

3.1.1 Typical structures Simple sequences

• • •

• • •

• • •

21

Typical structures ...

Parallel processes

• • •

• • •

• • •

Producer- Consumer (unbounded buffer)

• • •

• • •

cap

process 1

process 2

ta

tb

pa

pb

pc

tc

22

Typical structures ... Master - Slave

Resource Management

• • •

• • •

process 2

process 1

pc

tc

pb

pata

tb pd

process 1

process 2

ta

tb

pa

pb

pr

•

•

•

writers

readers

ta

tb

pa

pb

pr

•

n

n

n n

mutual exclusion one kind multiple resources

– single resource – reader / writers

23

Resource Management

ta tbpa pb

pr

••

•

- multiple processes; shared

resources: Philosophers problem

- sequential mutual exclusion

M1

T1 T5

T4

T3

T2

A1

M2

M3 M4

M5

A2

A3 A4

A5

24

3.1.2 Models of buffers Bounded buffer Two producers , Two kindwith capacity C two consumers of products

te

p1

ts

pcap Cpcap

p1

ts1te1

te2 ts2

C

FIFO buffer

tea

pcap

pa

pb

C

teb tsb

tsa

te ts

pnp1

•

p2

• •

• • •

t1 t2 tn-1

teb

pbnpb1

•

pb2

• •

• • •

t1b t2b tn-1b

tea

panpa1 pa2• • •

t1a t2a tn-1a tsa

tsb

FIFO buffer (two kind of products)

25

Models of buffers

te

p1

•

te1

p1

•

p2

•

pn

•

p3

•

• •

•

•

•

•

•

•

•

•

•

te2

te3

ten

ts1

ts2

ts3

tsn

Circular FIFO buffer LIFO buffer

•

•

•

•

•

•

p1

p2

p3

pn

te1 ts1

te2 ts2

te3 ts3

ten tsn

•

3.1.3 Models of miscellaneous DES

Chemical Batch Process

Product 1: A R1; B R1;Reaction;Discharge

Product 2: C R2;B R2;A R2;

Reaction;Discharge

27

Chemical Batch Process

A-R1

B-R1

Reacc 1

Desc 1

C-R2

B-R2

A-R2

Reacc 2

Desc 2

A disp

B disp

R1 vacio R2 vacio- PN model

28

A simple communication protocol

p1

p2

p3 p4

p5

p6 p7p8

t1

t2

t3t4

t5 t6

• •

Job Shop – routing and sequencing

M1 M2A1 A2 A3

Oper22

NP1

NP2

Oper12

Oper11 Oper21

• •

29

Traffic control

asd asd

TA TB

V0 V1 V2

V3V4V5

V6

•

•

• • •

V0 V1 V2 V3 V4 V5 V6 V0

T A0 T A1 T A2 T A3 T A4 T A5

T B0 T B1 T B2 T B3 T B4 T B5 T B6

T A6

30

4 PN extensions

4.1 Timed PN4.2 Coloured PN4.3 n-LNS (Hierarchical nets)

Curso COSNET 2002ESPECIFICACION Y ANALISIS FORMALES

DE SISTEMAS CON REDES DE PETRI

4.3 n-LNS Formalism

a

NET1

NET4(2)

NET3(1)

b

NET2(1

)

b a

NET4(1)

b

c2

c1 c3

c1

c2

c2

a

a, c

NET3(2)

NET2(2)

c

c NET3(3)

NET4(3)

NET3(4)

a

c3

c2

c2

c1

c3

x, y

x

.

.

.

x

y

.

.

.

y

x

<lab>

<lab><lab>

<lab>

<lab><lab><lab>

<lab>

<lab><lab>

<lab>

4.3 n-LNS Formalism

5. Sistema de Tráfico UrbanoModelado con PN 3-LNS.

5.1 Urban Traffic System(UTS)

Políticas de Tránsito y

Estrategias de Control MAX

50

INPUTS

Urban Traffic control

OUTS

Density

Flow

Average

Velocity

Travel Time

Average

Length

Queue

Level 3

Level 2

Level 1Street Network, Static Informative Objects

Intelligent Entities

Activities, Proccess,

Skills

MAX

50

5.2 UTS Hierarchical Functional Levels

5.2 Elementos del Modelo: SegmentoNivel 1

Red Vial, Objetos de Información estáticos

MAX

50Obji = (typei, valuei, wi)

(Oi, typeSi, ai, bi)

s1

si=

s2s5

s4s3

s6

s8 s9

s11 s12

s10

s7

Descripción de Segmento



MAX



s1

si=

s2s5

s4s3

s6

s9

s11 s12

s10

s7


t4,3

t3,4

t3,2

t2,3

t0,3 t3,0

t3,6t6,3

p3



MAX



s1

si=

s2s5

s3

s6

s8 s9

s11 s12

s10

s7


t11,7

t10,11

t11,10

p11

t7,11

39

( Environment net of type typeUrban1,1 )

Hidalgo_W

Alcalde_N

Hidalgo_EHidalgo_Alcalde

Alcalde_S

t6

t5

t2

t1

t4

t3

{t4}={cis4}

[cis3 ↓yi]

{t1}={ce}

{t5}={nci}

(Hidalgo_W)

(Alcalde_N)

(Hidalgo_E)

(Alcalde_S)

{t6}={nci}

{t2}={ce}

{t3}={cis3}

[nci↓x+yi][nci

↓x]

[nci↓x+yi]

[nci↓x]

[ce↓yi] [ce↓

yi]

[ce↓yi]

[ce↓yi]

[cis3 ↓yi]

[cis4 ↓yi]

[cis4 ↓yi]

(Hidalgo_Alcalde)

5.3. UTN modeled with 3-LNS.

{t1}={t2}={ce} {t4}={cis4}

{t3}={cis3} {t5}= {t6} = {nci}

(Hidalgo_W) = (Alcalde_N) =

(Hidalgo_E) =

(Hidalgo_Alcalde) =

(Alcalde_S) =

{ typeStreet2,1,typeCar2,1}.

Hidalgo_W

Hidalgo_E

Alc

ald

e_

N

Alc

ald

e_

S

((Hidalgo_W,t1), ce↓) = ((Alcalde_N,t2), ce↓) =

((Alcalde_S,t4), cis4↓) = ((Alcalde_S,t3), cis3↓)

= ((t1,Alcalde_S), ce↓) = ((t2,Alcalde_S), ce↓)

= ((t3,Hidalgo_E), cis3↓) =

((t4,Hidalgo_Alcalde), cis4↓) = yi

((t5,Hidalgo_W), nci↓) = ((t6,Alcalde_N), nci↓) =

x+yi

((Hidalgo_W,t5), nci↓) = ((Alcalde_N,t6), nci↓) =

x .

Net type typeCar2,2Net type typeStreet2,1

Nivel 2

Entidades

Inteligentes

5.4 Elementos del Modelo: EntityNET2,1

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS

INTERACTINGinitInteraction

endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity

t1 updatedProcess t3

DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

t10t11

5.4 Elementos del Modelo: ProcessNET3,1

initArrivalSegment,

initSenseAdvancing,

initLeaveSegment,

initChangeLane

initArrivalLane

updatedProcess

t1

initSenseStopped

updatedProcess

t2

initStart,

initChangeLane

t3

initStop

t4

STOPPED

p2

ADVANCINGp1

entityi

entityi = (ATTRi, PARAMi, knowledgeBasei)

ProcessNET3,1

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Nivel 3

Actividades,

Habilidades,

Procesos

5.6 Elementos del Modelo: SkillFreeFollowNET3,11

t6

p4

(t6)={initSenseAdvancing≡}(t5)={initSenseStopped≡}

t5

p6

(t8) ={newStart↑}

t8

p7

t9

(t9)={newSenseAdvancing↑}

φ(t2)={searchObstacle}

p3

NO_OBSTACLE

t2t1

λ(t1)={useSkillFreeFlow↑}

p1

λ(t10)={updatedProcess↑≡}

λ(t11)={unUsedSkill↑}t11

p9

λ(t7)={useSkillCarFollowing↑}

t3 t4

OBSTACLE

p2

p5

p8

t10

t7

SkillFreeFollowNET3,11

φ:T→2LABELi,k

Mecanismo de toma

de decisión

asociado

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Nivel 3

Actividades,

Habilidades,

Procesos

5.7 Elementos del Modelo: SkillCarFollowingNET3,11

p2

t3

φ(t2)={evalStop}

p8

p6

φ(t5)={evalSafeBreak}

t1


p1

NO_STOPSTOP

SAFE

NO_CHANGE

λ(t19)={updatedProcess,↑≡}

λ(t22)={unUsedSkill↑}

t19

p17

(t11)={newStop↑}

(t15)={newSenseStop, ↑}

(t12)={newCrash↑}

(t16)={newSenseCrash↑}

φ(t6)={evalChangeLane}


SAFE

t21

p16(t20)={initSenseStopped≡}

t20

p18(t23)={newStart↑}

t23

p19

t24


(t21)={initSenseAdvancing≡}

λ(t14)={useSkillChangeLane↑}

CHANGE

t2

t4

p5p4

t6t5

NO_SAFE

p15

p12

t22

t15

t11

t7 t8

t9 t10

t12

t13

t14t16 t17

t18

p3

p7

p9

p10 p11

p13 p14

φ:T→2LABELi,k

Mecanismo de toma

de decisión

asociado

SkillCarFollowingNET3,11ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Nivel 3

Actividades,

Habilidades,

Procesos

t2

φ(t2)={gapAcceptance}

p2 p3t1


NO_GAP

NO_SAFE_GAP

SAFE_GAP

p1

λ(t4)={initSenseStopped≡}

λ(t6)={newStartActivity↑}

λ(t5)={initSenseAdvancing≡}

λ(t7)={newChangeLaneActivity↑}


λ(t9)={newArrivalLaneActivity↑}

λ(t10)={updatedProcess↑≡}λ(t11)={unUsedSkill↑}

t28

t12

t3

t4

t5

t6

t7

t8

t9

t10

t11

p25

p11

p4

p5

p6

p7

p8

p9

p10

φ(t29)={evalSituation}

φ(t13)={evalSituation}

t13p12

t23

p13

t14

p13

CARE

DON’T_CARE

t15 p14

t16 p15

p22

t19

p18

SAFE

NO_SAFE

p16 p17

p19 p20

t24

t25

t26

t27

p23p24

λ(t24)={initSenseStopped≡}

λ(t25)={initSenseAdvancing≡}

λ(t24)={newStartActivity↑}


λ(t27)={newArrivalLaneActivity,↑}

(t17)={newStop↑}

(t18)={newSenseStop↑}

(t20)={newCrash↑}


p21

λ(t22)={newInConflict↑}

φ(t15)={safeBreak}

t30 p26

DON’T_CARE

p27 p28

(t31)={newCrash↑}


t17 t18

t20 t21

t22

t29 t31 t32

t33

p29

5.8 Elementos del Modelo: SkillChangeLaneNET3,12

φ:T→2LABELi,k

Mecanismo de toma

de decisión

asociado

SkillChangeLaneNET3,12.ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Nivel 3

Actividades,

Habilidades,

Procesos

5.9 Elementos del Modelo: ActivityNET3 Nets

ActivityNET3,1

(t3)={useSkillFreeFlow↑}

END

(t4)={endActivity↑}

ENQUEUED EVENT

p2t1

(t1)={initStart↑}

p1 p3t2

σ(t2)={position}

t3


END


ENQUEUED EVENT

p3t1

(t1)={initStop↑}

p1 p4p5t3

t5

σ(t2)={velocity}

t4t2

σ(t3)={position}

p2

p4

t4

StartActivityNET3,2

StopActivityNET3,3

StartActivityNet3,2, StopActivityNet3,3, ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Nivel 3

Actividades,

Habilidades,

Procesos

5.10 Metodología de Modelado

t0,1

t1,0

t1,4

t4,1

t5,4

t4,5

t9,5

t5,9

t7,9

t9,7

t11,7

t7,11

t4,3

t3,4

t7,6

t6,7

t10,6

t10,11

t6,10

t8,6

t6,8

t3,2

t2,3t2,8

t8,2

t0,3 t3,0

t3,6

t6,3 t7,4

t4,7

t11,10

p0 p1

p2p3 p4

p5

p8 p6 p7 p9

p10p11

MAX

50

s1

s2s5

s4s3

s6

s8 s9

s11 s12

s10

s7

47

5.11 Conclusion and Future work.

Phase 1.p2

p3

p4

p5

t6

t2

t4

t3

{t4}={cis5}

[cis5ci]

[cis5ci]

(p2)={typelight,typecar,typestreet}


{t6}={nci}

[cis

3

c i]

[cis

3

c i]

[cis2ci]

[cis2ci] {t2}={cis2}

{t3}={cis5}

p1

t5

t1

{t1}={cis1}

[cis

1

c i]

[cis

1

c i]

{t5}={nci}


AgentStreet_1CLOCK_1




Agentintersection_1CLOCK

6. Modelado de Sistemas Multi-agentes PN 3-LNS

Sistemas Multi-Agente

El ambiente del sistemaObjetos en el sistema (“pasivos” o agentes estacionarios)Agentes ( con su modelo de comportamiento y características)

Interacciones entre los agentes y el ambienteInteracciones entre los agentes y los objetosInteracciones entre agentes

Sistema Orientado a Eventos

Sistema

Evento 1

Evento 2

Evento 3Parámetros del Sistema

Tiempo Programado ATiempo Programado B

{Variable de estado cambiado}

{Variable de estado ∂ cambiado}

{Variable de estado α cammbiado}

Caso de Estudio

Estación de tren Colas

Colas

Colas

Tramo de vía

Vía Peatonal

Objetos Informativos Estacionarios

Entidad Inteligente (peatón)

Objetivo

Entidad Inteligente (tren)

1er Nivel de Abstracción


Colas

Colas

Tramo de vía

Vía Peatonal

Objetos Informativos Estacionarios

Objetivo

Nivel 1

Red Vial, Objetos de Información

Dinámicos y estáticos

2do Nivel de Abstracción


Colas

Colas

Entidad Inteligente (peatón)

Entidad Inteligente (tren)

Nivel 2

Entidades

Inteligentes

3er Nivel de Abstracción


Colas

Colas

Nivel 3

Actividades,

Procesos,

Habilidades

EnvironmentNet1

Obji = (typei, valuei, wi)

EntityNET2,1

(Oi, typeSi, ai, bi) si=

Descripción de Segmentodisplace

t21

t1

p9

p1

ESTACION1

p7

p8

displace

PUNTO_INFORMATIVO2

ESTACION2

ESTACION3

PUNTO_INFORMATIVO3PUNTO_INFORMATIVO4

ENTRADAPUNTO_INFORMATIVO1

PUNTO_INFORMATIVO5

t2

t3

t4

t5 t6 t7

t8

t9

t10t11

t12

t13

t14

t15

t16 t17

t18 t19

t20

p2p3

p4

p5

p6

displace

displace

displace

displace

displace

displacedisplace

displace

displace

displace

onBoard

unBoard

onBoard

unBoard

onBoard

unBoard

displace

displace

displace

EntityNET2,1ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

Entidades Inteligentes

ProcessNET3,1

entityi = (ATTRi, PARAMi, knowledgeBasei)

ProcessNET3,1

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

initStop

t2

initWalk

t3

p2

WALKINGp1

TRAVELLING

p3

boardBus

t1

unboardBus

t4

STOPPED

Base de ConocimientoID Regla Condición Acción

R1A IF spatialSituation[actori] == trafficLight

AND Event[actori] == yellowToRed AND

temporalRelation[actori, yellowToRed] ==

After

THEN stop(actori.arrivalTime, actori.currentPosition +

actori.traveledDistance+ actori.safeDistance,segmenti,

actori), start (Event[actori].time +

actori.getDelayToStart,segmenti, actori)

R1B IF spatialSituation[actori] ==

trafficLight AND Event[actori] ==

yellowToRed AND temporalRelation[actori,

yellowToRed] == Before

THEN leaveLink(actori.arrivalTime,

actori.currentPosition + actori.traveledDistance,segmenti,

actori), arrivalLink (actori.arrivalTime, 0.0,segmenti,

actori)

R2A IF spatialSituation[actori] ==


greenToYellow AND

temporalRelation[actori, greenToYellow] ==

After





R2B IF spatialSituation[actori] ==


greenToYellow AND

temporalRelation[actori, greenToYellow] ==

Before


actori.currentPosition + actori.traveledDistance,segmenti,

actori), arrivalLink (actori.arrivalTime, 0.0,segmenti,

actori)

R3A IF spatialSituation[actori] ==


redToGreen AND temporalRelation[actori,

redToGreen] == After


actori.currentPosition + traveledDistance,segmenti, actori),

arrivalLink (actori.arrivalTime, 0.0,segmenti, actori)

R3B

IF spatialSituation[actori] ==


redToGreen AND temporalRelation[actori,

redToGreen] == Before






t6

p4

(t6)={initSenseAdvancing≡}(t5)={initSenseStopped≡}

t5

p6

(t8) ={newStart↑}

t8

p7

t9


φ(t2)={searchObstacle}

p3

NO_OBSTACLE

t2t1

λ(t1)={useSkillFreeFlow↑}

p1

λ(t10)={updatedProcess↑≡}

λ(t11)={unUsedSkill↑}t11

p9


t3 t4

OBSTACLE

p2

p5

p8

t10

t7


φ:T→2LABELi,k

Mecanismo de toma

de decisión

asociado

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

SkillTrainFollowingNET3,11

p2

t3

φ(t2)={evalStop}

p8

p6


t1


p1

NO_STOPSTOP

SAFE

NO_CHANGE

λ(t19)={updatedProcess,↑≡}

λ(t22)={unUsedSkill↑}

t19

p17

(t11)={newStop↑}

(t15)={newSenseStop, ↑}

(t12)={newCrash↑}


φ(t6)={evalChangeLane}


SAFE

t21

p16(t20)={initSenseStopped≡}

t20

p18(t23)={newStart↑}

t23

p19

t24


(t21)={initSenseAdvancing≡}


CHANGE

t2

t4

p5p4

t6t5

NO_SAFE

p15

p12

t22

t15

t11

t7 t8

t9 t10

t12

t13

t14t16 t17

t18

p3

p7

p9

p10 p11

p13 p14

φ:T→2LABELi,k

Mecanismo de toma

de decisión

asociado

SkillTrainFollowingNET3,11

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

ActivityNET3 Nets

ActivityNET3,1


END


ENQUEUED EVENT

p2t1

(t1)={initStart↑}

p1 p3t2

σ(t2)={position}

t3


END


ENQUEUED EVENT

p3t1

(t1)={initStop↑}

p1 p4p5t3

t5

σ(t2)={velocity}

t4t2

σ(t3)={position}

p2

p4

t4

StartActivityNET3,2

StopActivityNET3,3

StartActivityNet3,2, StopActivityNet3,3,

ACTIVITIESPROCESS

EXEC_ACTIVITY

PROTOCOLS


endInteraction

sendReceive

endActivity

t4

t2

t8

p2p1

p4

p5

p6

SKILLS

p3

t6

t7

t5

initDecisionMaking

endSkill

initActivity


DECISION_MAKING

p7

useSkill

endActivity

t5t1

updatedProcess

t9

¿Preguntas?

Dr. Emmanuel López-Neri

[email protected]

Centro de Investigación, Innovación y Desarrollo Tecnológico

UVM Campus Guadalajara Sur.

mailto:[email protected]

Modelado de Sistemas con Redes de Petri 3-LNS...2 Resumen La finalidad de esta presentación es...

Documents

Transcript of Modelado de Sistemas con Redes de Petri 3-LNS...2 Resumen La finalidad de esta presentación es...