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:

    “Fear is cruel and mean. The political reigns of terror have been reigns of madness and malignity,—a total perversion of opinion; society is upside down, and its best men are thought too bad to live.”
    —Ralph Waldo Emerson (1803–1882)

    “With steady eye on the real issue, let us reinaugurate the good old “central ideas” of the Republic. We can do it. The human heart is with us—God is with us. We shall again be able not to declare, that “all States as States, are equal,” nor yet that “all citizens as citizens are equal,” but to renew the broader, better declaration, including both these and much more, that “all men are created equal.””
    —Abraham Lincoln (1809–1865)

    “... most Southerners of my parents’ era were raised to feel that it wasn’t respectable to be rich. We felt that all patriotic Southerners had lost everything in defense of the South, and sufficient time hadn’t elapsed for respectable rebuilding of financial security in a war- impoverished region.”
    —Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 1 (1962)

    “A life-long blessing for children is to fill them with warm memories of times together. Happy memories become treasures in the heart to pull out on the tough days of adulthood.”
    —Charlotte Davis Kasl (20th century)