1. DEVS Background DEVS = Discrete Event System Specification
Provides formal M&S framework: specification,simulation
Derived from Mathematical dynamical system theory
Supports hierarchical, modular composition
Object oriented implementation
Supports discrete and continuous paradigms
Exploits efficient parallel and distributed simulation techniques

2. Basic Entities and Relations in Modeling and Simulation
Experimental Frame
Device for
executing model
Real World
Simulator
Data: Input/output
relation pairs
simulation
relation
modeling
relation
Experimental frame specifies
conditions under which the system
is experimented with and observed
Model
Structure for generating behavior
claimed to represent real world
Each entity is represented
as a dynamic system
Each relation is represented
by a homomorphism or other
equivalence

3. DEVS Models There are two kinds of Models in DEVS Atomic Model
Coupled Model

4. DEVS Atomic Model Elements of an atomic model: input events
output events
state variables
state transition functions
External transition
Internal transition
Confluent transition
output function
time advance function

5. DEVS Atomic Model Formalism

6. Discrete Event Time Segmentsx x 1 X t0 t1 t2
(S,e) X Y S e y0 Y

7. 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.

8. Dynamic of Atomic Model
internal
Make a transition
(internal)
external
Make a transition
(external)
Handle input
input
State
time advance
Hold for
some time
output
Send an output

9. Atomic Model Examples Pulse out start Generator Pulse Generator
time
Pulse Generator
Output
interPulseTime >0
start
passive
active
ta = ∞
Fire-once Neuron
Output
Input
receptive
fire
refract
Firing delay >0
ta = ∞
ta = ∞
external event
Internal event
output event

10. The DEVSJAVA Example: carGenr, carWashCenter

11. Internal Transition /Output Generation
Generate output
using the
output
function
Time advance
using the
internal
transition
function s
Make a transition s’
Discussion: time advance =0, = Infinity

12. Response to External Input
Make a transition
using the
external
transition
function
elapsed
time
Time advance
Discussion: multiple inputs at the same time

13. Response to Simultaneous External Input and Internal Event
output
input
Generate output
Make a transition
elapsed
time
using the
confluent
transition
function
Time advance
Note: the output will be generated before the confluent function is executed

14. Discussion
There is no way to generate an output directly from an external input event. An output can only occur just before an internal transition.
To have an external event cause an output without delay, we have it “schedule” an internal state with a hold time of zero
The output function does not change a model’s state
In general, the only way to interact with a model is through input/output ports.
An implementation issue -- An atomic model works with any object-oriented classes
A coupled model does not have its own states or state transition functions.

15. genDevs.
modeling.
atomic
Basic Atomic Methods
public double ta() : the time advance function; returns the value of sigma for atomic models
public message out() : the output function; releases the message just before an internal transition
public void deltint(): the internal transition function
public void deltext(double e,message x): the external transition funciton
public void deltcon(double e,message x): the confluent transition function
public void Continue(double e) : subtract e from sigma; use to retain the same time of next event after an external event
public void holdIn(String phase, double sigma) : set the phase and sigma values as given in the arguments
public void passivateIn(String phase) : set the phase as given in the argument and sigma to INFINITY
public void passivate() : set the phase to passive and sigma to INFINITY
public boolean phaseIs(String phase) : return true if the current phase equals the argument
public double ta(){return sigma; }
public message out(){return new message()} //override
public void deltint() {} //override
public void deltext(double e,message x) {} //override
public void deltcon(double e,message x){}//default
deltint();
deltext(0,x); }
public void Continue(double e){
if (sigma < INFINITY)
sigma = sigma - e;
public void holdIn(String phase, double sigma) {
this.phase = phase;
this.sigma = sigma;;
public void passivateIn(String phase) {holdIn(phase, INFINITY);}
public void passivate() {passivateIn("passive");}
public boolean phaseIs(String phase){
return this.phase.equals(phase);

16. ignore all subsequent pulses
receptive
refract
input
fire
Firing delay >0
Output
Fire-once Neuron
This neuron fires exactly once after
a fixed delay while ignoring all subsequent inputs
public void initialize(){
super.initialize();
passivateIn("receptive"); }
public void deltext(double e,message x){
Continue(e);
if (phaseIs("receptive")&& somethingOnPort(x,"in"))
holdIn("fire",fireDelay);
ignore all subsequent pulses
pulse
pulse
pulse
pulse
input t
fire
Continue:
sigma = sigma - e
phase
state
receptive
refract
public void deltint(){
//if (phaseIs("fire"))
passivateIn("refract"); }
public message out(){
return outputNameOnPort("pulse","out");
sigma
pulseModels
foreOnceNeuron
elapsed
time
pulse
output

17. Basic Generator Concepts
pulseExpFrames.
basicGenr
second
Duration
third
Duration
First
Duration
first
second
passive
third
active
public void initialize(){
super.initialize();
holdIn("active",0); }
public void deltext(double e,message x){
Continue(e);
if (somethingOnPort(x,"start"))
holdIn("first",firstDuration);
else if (somethingOnPort(x,"stop"))
passivate();
public void deltint(){
if (phaseIs("active")) holdIn("first",firstDuration);
else if (phaseIs("first")) holdIn("second",secondDuration);
else if (phaseIs("second")) holdIn("third",thirdDuration);
else passivate(); }
public message out(){
if (phaseIs("active"))
return outputRealOnPort(firstOutput,"out");
else if (phaseIs("first"))
return outputRealOnPort(secondOutput,"out");
else if (phaseIs("second"))
return outputRealOnPort(thirdOutput,"out");
else //if (phaseIs("third"))
return outputRealOnPort(0,"out");

18. DEVS Coupled Model Elements of coupled model: Components
Interconnections
Internal Couplings
External Input Couplings
External Output Couplings

19. Coupling in Action output output internal external time advanceAB B A
Output
port
Input
port
external
State
internal
time advance
output
internal
external
State
time advance
output

20. DEVS Hierarchical Modular Composition
Atomic: lowest level model, contains structural dynamics -- model level modularity
SimpArc.efa
Coupled: composed of one or more atomic and/or coupled models
hierarchical construction
+ coupling

21. Coupled Model Example – Neuron net can compute the shortest path in a directed graph by mapping distances of edges to equivalent time values.
FireOnce
Neuron 1
Neuron 3
Neuron 2
pulseIn
pulseOut
Neuron 4
Pulse
Generator
Small network of fire-once neurons
a pulse emitted from the generator explores two paths concurrently to reach the final neuron (number 4).
depending on the summed firing delays along each path, a pulse emerging from one or the other will arrive first to the final neuron, the other will be shut out and prevented from continuing
in general, the clock time when a pulse first arrives to a neuron represents the shortest time to reach it
if nodes and link distances are mapped to neurons and firing times, then the path taken by a pulse represents the shortest path of an associated digraph.
the path can be reconstructed by extending the neuron model to allow retracing the path of earliest firings.
This method turns out to be isomorphic to the well known Dikstrai shortest path algorithm.
pulseModels.
fireOnce
NeuronNet
If instead of shortest paths, we request longest paths, a net of neurons that fire after their assigned fireDelays every time they receive a pulse will do the job. Finding critical paths in PERT charts require such longest path computation.

22. The DEVSJAVA Example: carWashSys

23. DEVS-based Modeling and Simulation
References:
B. P. Zeigler, Hessam S. Sarjoughian, Introduction to DEVS Modeling and Simulation with JAVA: Developing Component-Based Simulation Models,
B. P. Zeigler, H. Preahofer, T. G. Kim, Theory of Modeling and Simulation, New York, NY, Academic Press, 2000.

24. Homework
Read paper: DEVS Component-Based M&S Framework: An Introduction
Install DEVS JAVA and play with the example – look into the code
Research topic