Behavior of Coupled DEVS - View1: Total States = States * Elapsed Times

View1: Total States = States * Elapsed Times

Given a coupled DEVS model, its behavior is described as an atomic DEVS model

where

  • and are the input event set and the output event set, respectively.
  • is the partial state set where is the total state set of component (Refer to View1 of Behavior of DEVS), where is the set of non-negative real numbers.
  • is the initial state set where is the total initial state of component .
  • is the time advance function, where is the set of non-negative real numbers plus infinity.Given ,
    ta(s)= \min\{ ta_i(si) - t_{ei}| i \in D\}.


  • is the external state function. Given a total state where, and input event, the next state is given by

where

(s_i', t_{ei}')= \begin{cases} (\delta_{ext}(s_i, t_{ei}, x_i),0) & \text{if } (x, x_i) \in C_{xx}\\ (s_i, t_{ei}) & \text{otherwise}. \end{cases}

Given the partial state, let denote the set of imminent components. The firing component which triggers the internal state transition and an output event is determined by

  • is the internal state function. Given a partial state, the next state is given by

where

(s_i', t_{ei}')= \begin{cases} (\delta_{int}(s_i),0) & \text{if } i = i^*\\ (\delta_{ext}(s_i, t_{ei}, x_i),0) & \text{if } (\lambda_{i^*}(s_{i^*}), x_i) \in C_{yx}\\ (s_i, t_{ei}) & \text{otherwise}. \end{cases}
  • is the output function. Given a partial state ,
    \lambda(s)= \begin{cases} \phi &\text{if } \lambda_{i^*}(s_{i^*})=\phi \\ C_{yy}(\lambda_{i^*}(s_{i^*})) &\text{otherwise}. \end{cases}

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