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.

Algorithms

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 \ne 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 \le t  and  t \le 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)\ne \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

References