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Basic Entities and Relations in Modeling and Simulation

Experimental Frame

Source

Simulator

System

behavior database

Modeling

Relation

Simulation

Relation

Model

DEVS Formalism

DEVS = Discrete Event Systems Specification

- Atomic Models
- Coupled Models
- Hierarchical Models

DEVS Atomic Model

Elements of an atomic model:

- input events
- output events
- state variables
- state transition functions
- output function
- time advance function

Atomic Model Operation

- Ports are represented explicitly – there can be any number of input and output ports on which values can be received and sent
- The time advance function determines the maximum lifetime in a state
- A bag can contain many elements with possibly multiple occurrences of its elements.
- Atomic DEVS models can handle bags of inputs and outputs.
- The external transition function handles inputs of bags by causing an immediate state change, which also may modify the time advance.
- The output function can generate a bag of outputs when the time advance has expired.
- The internaltransition function is activated immediately after the output function causing an immediate state change, which also may modify the time advance.
- The confluent transition function decides the next state in cases of collision between external and internal events.

DEVS = <X,S,Y, dint , d ext ,dcon, ta,l >

X : a set of input events.

Y: a set of output events.

S: a set of states

ta :S-> R+0,inf time advance function

dint :S -> Sinternal transition function.

d ext :Q x Xb-> Sexternal transition function,

d con :Q x Xb-> Sconfluent transition function,

where Xb is a set of bags over elements in X.

Q= {(s,e)|se S, 0<= e<=ta(s)}

l:S -> Youtput function

DEVS Atomic Model Implements Basic DEVS

Make a transition

(internal)

Make a transition

(external)

input

State

internal

external

time advance

Handle input

output

output

Hold for

some time

Send an output

Internal Transition /Output Generation

output

Generate output

s’

Time advance

s

Make a transition

using the

output

function

using the

internal

transition

function

input

Make a transition

using the

external

transition

function

elapsed

time

Time advance

Response to Simultaneous External Input and Internal Event

output

input

Make a transition

Generate output

elapsed

time

using the

confluent

transition

function

Time advance

out

receptive

active

passive

fire

refract

Atomic Model Examplespulse

Pulse

Generator

time

Pulse Generator

interPulseTime >0

Output

start

ta = ∞

Output

Fire-once Neuron

Input

Firing delay >0

ta = ∞

ta = ∞

external event

Internal event

output event

Plan

Emergency

Phone

Call

Response

Basic DEVS: Example Scuba Model

=dint (“five”) for phase != “five” ,“surface1”, “surface2”

dint (“five”,s ) otherwise //except when already on “five

DEVS Hierarchical Modular Composition

Atomic: lowest level model, contains structural dynamics -- model level modularity

Coupled: composed of one or more atomic and/or coupled models

hierarchical construction

+ coupling

DN = < X,Y,D,{Mi },{Ii },{Zi,j }>

X : a set of input events.

Y: a set of output events.

D : an index set for the components of the coupled model.

For eachieD ,

Mi is a component DEVS model.

For eachieDu self, Iiis the set of influencees ofi .

For eachjeDu self ,

Zi,jis output translation mapping

class ef:public digraph{

public:

ef():digraph(){

genr * g = new genr("g);

transd * t = new transd("t");

add(g);

add(t);

ef

out

start

start

g

result

ariv

out

t

in

out

done

add coupling

add_coupling(this, "in", t, "done");

add_coupling(this, "start", g, "start");

t->add_coupling(t,"out",g,"stop");

t->add_coupling(t, "out", this, "result");

g->add_coupling(g, "out", this, "out");

g->add_coupling(g, "out", t, "ariv");

declare ports

inports->add("in");

outports->add("out");

inports->add("start");

outports->add("result");

DIGRAPH

inherits

can hold

ENTITY

Object Oriented

DEVS CLASSES

DEVS

ATOMIC

devs

COUPLED

MESSAGE

CONTAINER

content

entity

port,

value ->ENTITY

deltext(t-tN,m)

deltint()

deltcon(m)

Simulation Cycle for DEVS Parallel /Confluent

- Compute the global next event time, tN: use reduce to get minimum of component times to next event (tN)
- Tell all components the global tN and
- if component is imminent (tN == global tN ),
- then generate output message(using l)
- Sort and distribute (using coupling) output messages.
- Tell all components
- if component is imminent (tN == global tN )
- or has incoming mail (external events)
- or both
- then execute transition function (wrap_deltfunc).

(UI)

Tell_all (next_tN) Ensemble Message

+ 2

i

i

+ 1

compute tN

compute tN

return MIN tN

return MIN tN

+ 5

+ 6

i

i

+ 4

i

i

+ 3

compute tN

compute tN

compute tN

compute tN

return tN

return MIN tN

return MIN tN

return MIN tN

+ 10

i

i

+ 9

i

+ 7

compute tN

compute tN

compute tN

compute tN

compute tN

return tN

return tN

return tN

return tN

return tN

Simulation Cycle Step 1

Compute the next event time (tN) : uses reduction to get

minimum of the component times to next event.

Collection of Minimum tN Values

i

compute tN

return MIN tN

Low Node

+ 8

i

+ 11

i

High Node

Tell_all (compute_IO) Ensemble Message

i

+ 1

compute_IO

compute_IO

compute_IO

compute_IO

compute_IO

compute_IO

i

+ 7

compute_IO

compute_IO

compute_IO

compute_IO

compute_IO

Simulation Cycle Step 2

Tell all components global tN:

if component is imminent generate and sort output messages

i

compute_IO

Low Node

+ 2

i

+ 6

i

+ 5

i

+ 4

i

+ 3

i

i

+ 10

i

+ 9

+ 11

+ 8

i

i

High Node

+ 4

+ 3

i

+ 1

+ 2

i

i

+ 5

i

Step 1 : Mail Message Size Information

Step 2 : Mail Exchange

Mail Exchange in Step3

tell all imminents,

sort, and distribute output messages (mail) using coupling

Tell_all (wrap_deltfunc) Ensemble Message

i

+ 1

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

i

+ 7

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

wrap_deltfunc

Simulation Cycle Step 4

Tell all components with to execute their

transition functions.

i

wrap_deltfunc

Low Node

+ 2

i

+ 6

i

+ 5

i

+ 4

i

+ 3

i

i

+ 10

i

+ 9

+ 11

+ 8

i

i

High Node

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