Simulation algorithms for coupled DEVS

Given a coupled DEVS model, simulation algorithms are methods to generate the model's legal behaviors, which are a set of trajectories not to reach illegal states. (see behavior of a Coupled DEVS model.) [Zeigler84] originally introduced the algorithms that handle time variables related to lifespan $t_{s}\in [0,\infty ]$ and elapsed time $t_{e}\in [0,\infty )$ by introducing two other time variables, last event time, $t_{l}\in [0,\infty )$ , and next event time $t_{n}\in [0,\infty ]$ with the following relations:

\,t_{e}=t-t_{l}

and

\,t_{s}=t_{n}-t_{l}

where $t\in [0,\infty )$ denotes the current time. And the remaining time,

\,t_{r}=t_{s}-t_{e}

is equivalently computed as

\,t_{r}=t_{n}-t,

apparently $t_{r}\in [0,\infty ]$ .

Based on these relationships, the algorithms to simulate the behavior of a given Coupled DEVS are written as follows.

Algorithm

algorithm DEVS-coordinator
  Variables:
     parent // parent coordinator
      $t_{l}$ : // time of last event
      $t_{n}$ : // time of next event
      $N=(X,Y,D,\{M_{i}\},C_{xx},C_{yx},C_{yy},Select)$  // the associated Coupled DEVS model
    when receive init-message(Time t)
        for each  $i\in D$  do
            send init-message(t) to child  $i$ 
         $t_{l}\leftarrow \max\{t_{li}:i\in D\}$ ;
         $t_{n}\leftarrow \min\{t_{ni}:i\in D\}$ ;
    when receive star-message(Time t)
        if  $t\neq t_{n}$  then
            error: bad synchronization;
         $i^{*}\leftarrow Select(\{i\in D:t_{ni}=t_{n}\});$ 
        send star-message(t)to  $i^{*}$ 
         $t_{l}\leftarrow \max\{t_{li}:i\in D\}$ ;
         $t_{n}\leftarrow \min\{t_{ni}:i\in D\}$ ;
    when receive x-message( $x\in X$ , Time t)
        if  $(t_{l}\leq t$  and  $t\leq t_{n})$  == false then
            error: bad synchronization;
        for each  $(x,x_{i})\in C_{xx}$  do
            send x-message( $x_{i}$ ,t) to child  $i$ 
         $t_{l}\leftarrow \max\{t_{li}:i\in D\}$ ;
         $t_{n}\leftarrow \min\{t_{ni}:i\in D\}$ ;
    when receive y-message( $y_{i}\in Y_{i}$ , Time t)
        for each  $(y_{i},x_{i})\in C_{yx}$  do
            send x-message( $x_{i}$ ,t) to child  $i$ 
        if  $C_{yy}(y_{i})\neq \phi$  then
            send y-message( $C_{yy}(y_{i})$ , t) to parent;
         $t_{l}\leftarrow \max\{t_{li}:i\in D\}$ ;
         $t_{n}\leftarrow \min\{t_{ni}:i\in D\}$ ;

References

[Zeigler84] Bernard Zeigler (1984). Multifacetted Modeling and Discrete Event Simulation. Academic Press, London; Orlando. ISBN 978-0-12-778450-2.
[ZKP00] Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000). Theory of Modeling and Simulation (second ed.). Academic Press, New York. ISBN 978-0-12-778455-7.

Algorithm

See also

References