ECE 449/549

Class Notes #2

Introduction to Discrete-Event Systems Specification (DEVS)

Sept. 2008

Source System Simulator

Model

Experimental Frame

SimulationRelation

ModelingRelation

behavior database

Basic Entities and Relations in Modeling and Simulation

DEVS Formalism

DEVS = Discrete Event Systems Specification

• Atomic Models

• Coupled Models

• Hierarchical Models

x0 x1X

S

Yy0

e

t0 t1 t2

Discrete Event Time Segments

DEVS Atomic Model

• input events

• output events

• state variables

• state transition functions

• output function

• time advance function

Elements of an atomic model:

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 internal transition 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 = DEVS = <X,S,Y, <X,S,Y, int int , , ext , ext ,con, con, ta,ta,

XX : a set of input events.

YY : a set of output events.

SS : a set of states

ta :ta : SS R R++0,inf 0,inf time advance function

int int ::S S S S internal transition function.

ext ext ::Q x XQ x Xbb S S external transition function,

con con ::Q x XQ x Xbb S S confluent transition function,

where XXbb is a set of bags over elements in XX.

Q= {(s,e)|sQ= {(s,e)|sS, 0S, 0 e e ta(s)}ta(s)} :: S S Y Y output function

Basic specification:Basic specification:

State

output

external internal

time advance

Make a transition(external)

Make a transition(internal)

Handle input

Send an output

Hold for some time

input

output

DEVS Atomic Model Implements Basic DEVS

Internal Transition /Output Generation

s

Generate output

output

Make a transitions’

Time advance using theinternaltransitionfunction

using theoutputfunction

Time advance

input

Make a transition

Response to External Input

elapsedtime

using theexternaltransitionfunction

Time advance

input

Make a transition

Response to Simultaneous External Input and Internal Event

elapsedtime

Generate output

output

using theconfluenttransitionfunction

receptive refractInput

fireFiring delay >0

Output Fire-once Neuron

Atomic Model Examples

PulseGenerator

out

pulse

time

passive activestart

interPulseTime >0Output Pulse Generator

start

external event Internal event output event

ta = ∞

ta = ∞ ta = ∞

Basic DEVS: Example Scuba Model

60ft35 min

1 hr

40ft25 min

5 min5ft

Dive Plan

EmergencyPhone

Call Response

=dint (“five”) for phase != “five” ,“surface1”, “surface2”dint (“five”,s ) otherwise //except when already on “five

DEVS Hierarchical Modular CompositionAtomic: lowest level model,

contains structural dynamics -- model level modularity

Atomic

Atomic Atomic

Atomic

+ coupling

Atomic

Atomic

Atomic

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

construction

DN = < DN = < XX ,Y,D,{M,Y,D,{Mi i },},{I{Ii i },},{Z{Zi,j i,j }}

XX : a set of input events.

YY : a set of output events.

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

For each ii DD ,

MMi i is a component DEVS model.

For each ii DD selfself , IIii is the set of influencees of ii .

For each jj DD selfself ,

ZZi,ji,j is output translation mapping

Coupled model specification:Coupled model specification:

class ef:public digraph{ public:ef():digraph(){ genr * g = new genr("g); transd * t = new transd("t");

add(g); add(t);

create componentscreate components

gg

tt

donedone

startstart

arivariv outout

efefoutout

inports->add("in"); outports->add("out"); inports->add("start"); outports->add("result");

declare portsdeclare ports

inin

startstart

resultresult

outout

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");

add couplingadd coupling

DIGRAPHDIGRAPH

DEVSDEVS

ENTITYENTITY

CONTAINERCONTAINER

ATOMICATOMIC

COUPLEDCOUPLED

devsdevs

entityentity

LegendLegend

inherits

can hold

Object Oriented DEVS CLASSES

MESSAGEMESSAGE

contentcontent port, value ENTITY

Simulation Cycle for DEVS Parallel /Confluent

1 Compute the global next event time, tN: use reduce to get minimum of component times to next event (tN)

2 Tell all components the global tN and

if component is imminent (tN == global tN ),

then generate output message(using )

3 Sort and distribute (using coupling) output messages.

4 Tell all components

if component is imminent (tN == global tN )

or has incoming mail (external events)

or both

then execute transition function (wrap_deltfunc).

wrap_deltfunc(t,m)

deltcon(m)deltint()deltext(t-tN,m)

Simulation Cycle Step 1Compute the next event time (tN) : uses reduction to get minimum of the component times to next event.

Tell_all (next_tN) Ensemble Message

compute tN

compute tN compute tN

compute tN compute tN compute tN compute tN

compute tN compute tN compute tN compute tN compute tNreturn tN return tN return tN return tN return tN

return MIN tN return MIN tN return MIN tN return tN

return MIN tN return MIN tN

return MIN tN

Collection of Minimum tN Values

Low Node

High Node

i

+ 8

+ 1i + 2i

+ 3i + 4i + 5i + 6i

+ 7i i + 9i i + 11+ 10i

Block(UI)

Simulation Cycle Step 2

Tell_all (compute_IO) Ensemble Messagecompute_IOLow Node

High Node

i

+ 8

+ 1i + 2i

+ 3i + 4i + 5i + 6i

+ 7i i + 9i i + 11+ 10i

compute_IO compute_IO

compute_IO compute_IO compute_IO compute_IO

Tell all components global tN: if component is imminent generate and sort output messages

compute_IO compute_IO compute_IO compute_IO compute_IO

Mail Exchange in Step3

+ 1i + 2i + 3i + 4i + 5i

tell all imminents,sort, and distribute output messages (mail) using coupling

Step 1 : Mail Message Size Information

Step 2 : Mail Exchange

Simulation Cycle Step 4

Tell_all (wrap_deltfunc) Ensemble Messagewrap_deltfuncLow Node

High Node

i

+ 8

+ 1i + 2i

+ 3i + 4i + 5i + 6i

+ 7i i + 9i i + 11+ 10i

wrap_deltfunc wrap_deltfunc

wrap_deltfunc wrap_deltfunc wrap_deltfunc wrap_deltfunc

wrap_deltfunc wrap_deltfuncwrap_deltfuncwrap_deltfuncwrap_deltfunc

Tell all components with to execute their transition functions.