Atomic DEVS

An atomic DEVS model is defined by a 7-tuple structure

$$A=<X,Y,S, s_0, \tau, \delta_x, \delta_y>$$

where

• $X$ is a set of input events.
• $Y$ is a set of output events.
• $S$ is a set of states.
• $s_0 \in S$ is the initial state.
• $\tau:S \rightarrow T$ is the time advance function where $T=[0,\infty]$ is the set of non-negative real numbers plus the transfinite number, infinity. This function is used to determine the lifespan of a state.
• $\delta_x: P \times X \rightarrow S \times \{0,1\}$ is the input transition function where
  $$P=\{(s, t_s, t_e)\vert s \in S, t_s \in T, t_e \in [0,t_s] \}$$
  is the set of states with times such that $t_s$ and $t_e$ are the lifespan of the state, $s$ , and the elapsed time since the last reset of $t_e$ , respectively. $\delta_x$ defines how an input event, $x$ , changes a state as well as the lifespan that the system can be in that state and the elapsed time that the system has been in that state.
• $\delta_y: S \rightarrow Y \times S$ is the output transition function that defines how a state generates an output event and, at the same time, how it changes the state internally. This function can be invoked when the elapsed time reaches the lifespan. ^2.1 $\blacksquare$

Figure 1.1: Symmetric Structure of Atomic DEVS

Figure 1.1, also used as the cover illustration, shows the symmetric structure of DEVS in the sense that the input event set ($X$ ) and the input transition function ($\delta_x$ ) are on the input side; the output event set ($Y$ ) and the output transition function ($\delta_y$ ) are on the output side; and a set of states ($S$ ) and its time advance function ($\tau$ ) are in the middle.