Simulation algorithms for atomic DEVS

Regardless of two different views of total states, algorithms for initialization and internal transition cases are commonly defined as below.

DEVS-simulator
  variables:
    parent // parent coordinator
    ${\displaystyle t_{l}}$     // time of last event
    ${\displaystyle t_{n}}$     // time of next event
    ${\displaystyle A=(X,Y,S,ta,\delta _{ext},\delta _{int},\lambda )}$// the associated Atomic DEVS model 
  when receive init-message(Time ${\displaystyle t}$)
     ${\displaystyle t_{l}\leftarrow t;}$
     ${\displaystyle t_{n}\leftarrow t_{l}+ta(s);}$
  when receive star-message(Time ${\displaystyle t}$)
     if ${\displaystyle t\neq t_{n}}$ then
        error: bad synchronization;
     ${\displaystyle y\leftarrow \lambda (s);}$
     send y-message(${\displaystyle y,t}$) to parent;
     ${\displaystyle s\leftarrow \delta _{int}(s)}$
     ${\displaystyle t_{l}\leftarrow t;}$
     ${\displaystyle t_{n}\leftarrow t_{l}+ta(s);}$

As addressed in Behavior of Atomic DEVS, when DEVS receives an input event, right calling ${\displaystyle \delta _{ext}}$, the last event time,${\displaystyle t_{l}}$ is set by the current time,${\displaystyle t}$, thus the elapsed time${\displaystyle t_{e}}$ becomes zero because ${\displaystyle t_{e}=t-t_{l}}$.

  when receive x-message(${\displaystyle x\in X}$, Time ${\displaystyle t}$)
     if ${\displaystyle (t_{l}\leq t}$ and ${\displaystyle t\leq t_{n})}$ == false then
        error: bad synchronization;
     ${\displaystyle s\leftarrow \delta _{ext}(s,t-t_{l},x)}$
     ${\displaystyle t_{l}\leftarrow t;}$
     ${\displaystyle t_{n}\leftarrow t_{l}+ta(s);}$

Notice that as addressed in Behavior of Atomic DEVS, depending on the value of ${\displaystyle b}$ return by ${\displaystyle \delta _{ext}}$, last event time,${\displaystyle t_{l}}$, and next event time,${\displaystyle t_{n}}$,consequently, elapsed time, ${\displaystyle t_{e}}$, and lifespan${\displaystyle t_{n}}$, are updated (if ${\displaystyle b=1}$) or preserved (if ${\displaystyle b=0}$).

  when receive x-message(${\displaystyle x\in X}$, Time ${\displaystyle t}$)
     if ${\displaystyle (t_{l}\leq t}$ and ${\displaystyle t\leq t_{n})}$ == false then
        error: bad synchronization;
     ${\displaystyle (s,b)\leftarrow \delta _{ext}(s,t-t_{l},x)}$
     if ${\displaystyle b=1}$ then 
        ${\displaystyle t_{l}\leftarrow t;}$
        ${\displaystyle t_{n}\leftarrow t_{l}+ta(s);}$

• Atomic DEVS
• Behavior of atomic DEVS
• Simulation algorithms for coupled DEVS

• [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.