Review

A_D A_A

Ball_A

Ball_B

player_A B_D B_A

Ball_B

Ball_A

player_B

Ball_A Ball_A

Ball_B Ball_B

A_A, B_D A_D, B_A

Ball_A

Ball_B

CFSM

Player_A : X S SXA = {Ball_A}{} : internal event

A_A A_D

/Ball_A

A_A A_D

Ball_A feedback

CFMS for the ping-pong example

A_A A_DBall_B

Ball_ABall_B

Ex) ping-pong game

– (i) what if “attack” takes 2 steps: one state generating output, other state with no output. State independent of any

inputs.– (ii) what if we want to specify time to be spent for state A or D

– A takes 0.1sec. (A’s control : output)– D takes ? sec (B’s control : output)

• input event -> state transition

• time modeling Infinity

• No semantics for such sojourn time specification:

logical time models.

A_A A_DBall_B

Ball_ABall_B

A_A

R_B

A_A

Receiving state

A_A

A_DBall_B

Ball_A

Ball_B

R_B

Ball_A

?replace

Limitation of expressive power in FSM

internal transition & time advance function(defined)• introducing internal transition function

int : S S

• introducing time advance functionta : S R+

0,

Solution : DEVS (Discrete Event System Specification) Formalism

What is DEVS?

• DEVS = Discrete Event System Specification

• Provides sound formal M&S framework

• Supports full range of dynamic system representation capability

• Supports hierarchical, modular model development

(Zeigler, 1976/84/90/00)

DEVS Modeling & Simulation Framework

Separates Modeling from Simulation Derived from Generic Dynamic Systems

Formalism– Includes Continuous and Discrete Time

Systems Provides Well Defined Coupling of Components Supports

– Hierarchical Construction– Stand Alone Testing– Repository Reuse

Enables Provably Correct, Efficient, Event-Based, Distributed Simulation

The DEVS Framework for M&S

Formalism transformation

DEVS Formalism Discrete-Event formalism: time advances using a

continuous time base.

Basic models that can be coupled to build complex simulations.

Abstract simulation mechanism

Atomic Models:

M = < X, S, Y, int, ext, , D >.

Coupled Models:

CM = < X, Y, D, {Mi}, {Ii}, {Zij}, select >

Atomic model definition

Behavioral models

DEVS Atomic models

Atomic DEVS = < S, X, Y, int ,ext , , ta >• X : external input event set

• Y : external output event set

• S : sequential state set int: internal transition function

ext :external transition function

: output function

• ta : time advance function

• ta : S R+0,

• Q = {(s,e) | s S, 0 e ta(s)} : total state set, e: elapsed time

int : S S

ext : X * Q S

: S Y

S

int

ext

R

X Y

DEVS Atomic models (cont.)

External Event Transition Function (ext): transforms state

and an input event into another state(e.g., receiving a faulty device, put it into a queue to await its turn for repair.)

Output Function (): maps a state into an output (e.g., number of parts available falls below a minimum

number, issue an order to restock.)

Internal Event Transition Function (int): transforms state

into another state after time has elapsed(e.g., there are 10 parts available and broken part requires

7 of them, after fixing broken part, 3 parts will remain.)

Time Advance Function (ta): maps a state into a duration (e.g., how long to fix a device once processing has started.)

Atomic model Discrete Event Dynamics

ta(s) ta(s) (1)(1)ss

DEVS = DEVS = < X, S, Y, < X, S, Y, int int , , ext ext , ta, , ta,

ss

y y (3)(3)

ss’ ’ = = int int ss

x x (5)(5)

ss’ ’ = = ext ext ((s,e,x)s,e,x)

(6)(6)

DEVS atomic models semantics

ta(s) ta(s) (1)(1)ss

DEVS = DEVS = < X, S, Y, < X, S, Y, int int , , ext ext , ta, , ta,

ss

y y (3)(3)

ss’ ’ = = int int ss

x x (5)(5)

ss’ ’ = = ext ext ((s,e,x)s,e,x)

(6)(6)

DEVS atomic models semantics

– AMplayer_A =< S, X, Y, int ,ext , , ta >

• X = {Ball_B}

• Y = {Ball_A}

• S = {A, D} int (A) = D

ext (Ball_B, D) = A

• ta(A) = thinking_time

• ta(D) = INFINITY (A) = Ball_A

A DBall_B

Ball_ABall_B

Atomic model example: ping-pong

Moutin

event

t

x1 y1 x2

t

S

s0

s1

s2

s2=ext((s0,e),x1)s1=int(s2)

t

e

ta(s0)ta(s2)ta(s1)

Dynamic behavior of DEVS models