T-statistic

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 $t_s\in [0,\mathrm{\infty }]$ and elapsed time $t_e\in [0,\mathrm{\infty })$ by introducing two other time variables, last event time, $t_l\in [0,\mathrm{\infty })$, and next event time $t_n\in [0,\mathrm{\infty }]$ with the following relations:

$t_e=t-t_l$

and

$t_s=t_n-t_l$

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

$t_r=t_s-t_e$

is equivalently computed as

$t_r=t_n-t$

, apparently $t_r\in [0,\mathrm{\infty }]$.

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;
     $i^{\ast }\leftarrow Select(\{i\in D:t_{ni}=t_n\});$
     send star-message(t)to $i^{\ast }$
     $t_l\leftarrow max\{t_{li}:i\in D\}$;
     $t_n\leftarrow min\{t_{ni}:i\in D\}$;
  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 $C_{yy}(y_i)\ne \varphi$ 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] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• [ZKP00] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534