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;
        $t_{l}\leftarrow \max\{t_{li}:i\in D\}$;
        $t_{n}\leftarrow \min\{t_{ni}:i\in D\}$;

See also

• Coupled DEVS
• Behavior of Coupled DEVS
• Simulation Algorithms for Atomic DEVS

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.