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}

Read more about this topic:  Behavior Of Coupled DEVS

Famous quotes containing the words total, states, elapsed and/or times:

    “The only way into truth is through one’s own annihilation; through dwelling a long time in a state of extreme and total humiliation.”
    —Simone Weil (1909–1943)

    “The government of the United States is a device for maintaining in perpetuity the rights of the people, with the ultimate extinction of all privileged classes.”
    —Calvin Coolidge (1872–1933)

    “The quickness with which all the “stuff” from childhood can reduce adult siblings to kids again underscores the strong and complex connections between brothers and sisters.... It doesn’t seem to matter how much time has elapsed or how far we’ve traveled. Our brothers and sisters bring us face to face with our former selves and remind us how intricately bound up we are in each other’s lives.”
    —Jane Mersky Leder (20th century)

    “But this I know; the writer who possesses the creative gift owns something of which he is not always master—something that at times strangely wills and works for itself.... If the result be attractive, the World will praise you, who little deserve praise; if it be repulsive, the same World will blame you, who almost as little deserve blame.”
    —Charlotte Brontë (1816–1855)