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Review

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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

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ta(s) (1) s DEVS = < X, S, Y, int, ext, ta, s y (3) s ’ = int s x (5) s ’ = ext ( s,e,x) (6) (6) DEVS atomic models semantics

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M outin event t x1x1 y1y1 x2x2 t S s0s0 s1s1 s2s2 s 2 = ext ((s 0,e),x 1 ) s 1 = int (x 2 ) t e ta(s 0 )ta(s 1 ) ta(s 2 ) Dynamic behavior of DEVS models

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Atomic model example: Processing Server

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Coupled models Structural models (multicomponent)

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–Petri Net : incremental –DEVS : hierarchical GENBUFPROC out in out done GEN-BUF-PROC BUF-PROC G+B+P B+PG PB ABC Incremental : A and B: connect ABC Hierarchical : A and BC: connect BC ABC Hierarchical vs. Incremental modelling

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CM = n X is the set of input events; n Y is the set of output events; n D is an index for the components of the coupled model, and i D, M i is a basic DEVS model (that is, an atomic or coupled model), defined by M i = n IC is the set of Input Couplings; n EIC is the set of External Input Couplings; n EOC is the set of External Output Couplings; n Finally, select is the tie-breaking selector. Coupled models formal specification

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–GEN-BUF-PROC = X = ; Y = { out } I(GEN) = BUF; I(BUF) = PROC; I(PROC)= {BUF, self} Z(GEN)=BUF; Z(BUF)=PROC; Z(PROC) = BUF; Z(PROC)=self. SELECT : ({GEN, BUF, PROC}) = GEN ({BUF, PROC}) = BUF GENBUFPROC out in out done Coupled DEVS example

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DN X, Y, D, {M i }, {I i }, {Z i,j } DEVS X, S, Y, int, ext, con, ta, DEVS X, S, Y, int, ext, con, ta, Every DEVS coupled model has a DEVS Basic equivalent Closure Under Coupling

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n Components (D) n couplings –Internal Couplings (IC) –External Input Couplings (EIC) –External Output Couplings (EOC) repair shop out sent finished repaired faulty generator (genr) transducer (transd) out report stop start Input/output ports concepts

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–GEN-BUF-PROC = X = Y = { out } EIC = EOC = { (PROC.out, GEN_BUF_PROC.out) } IC = { (GEN.out, BUF.in), (BUF.out, PROC.in), (PROC.out, BUF.done)} SELECT : ({GEN, BUF, PROC}) = GEN ({BUF, PROC}) = BUF : GENBUFPROC out in out done Coupled DEVS example

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–Internal transition Model knows its schedule time (by time advance) –External transition Model doesn’t know its schedule time influencer’s schedule –Conflict case Internal and external events External events M1M1 M2M2 M 2 : M 1 ’s influencee M 1 : M 2 ’s influencer Concept of Scheduling and Tie-break

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GEN BUFFER PROC out in done * GEN = X = Y = {out} S = {G} int : int (G) = G ext :unavailable (G) = out ta(G) = GEN_TIME G (out, ta(G)) * PROC = X = {in} Y = {out} S = { B, F } int : int (B) = F ext : ext (F, in) = B (B) = out ta(B) = PROCESS_TIME BF (in,e) (out, ta(B)) BUF (coupled model) Tie-Breaking example BUFFER: Exercise

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–conflict schedule is resolved by assigning priority between models that cause schedules. Internal and external events External events –Sel : 2 {Mi} {M i } n,F out(BUF)in(GEN) Priority(BUF,GEN) = GEN n,B done(PROC)In(GEN) Priority(PROC,GEN) = GEN Tie-breaking

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ECE 449/549 Class Notes #1 Introduction to System Modeling Concepts and DEVS Sept. 2008.

ECE 449/549 Class Notes #1 Introduction to System Modeling Concepts and DEVS Sept. 2008.

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