1.3.1 Atomic DEVS

An Atomic DEVS is a functional atom in a model, which cannot be further divided into sub-components. Its behavior is described by implementation-independent mathematical functions and symbols.

Table 1.1: Atomic DEVS $<S,ta,\delta _{int},X,\delta _{ext},Y,\lambda >$

$S$	a set of admissible states
$ta:S\to R_{0,+\infty}^{+}$	time advance function
$\delta_{int}:S\to S$	internal transition function
$X$	a set of admissible external inputs
$\delta_{ext}:Q\times X\to S$	external transition function
	where $Q=\{(s,e)\vert s\in S,0 \leq e \leq ta(s)\}$
$Y$	a set of possible outputs
$\lambda:S\to Y\cup\{\o\}$	output function

Atomic DEVS is a tuple $<S,ta,\delta _{int},X,\delta _{ext},Y,\lambda >$ as shown in Table 1.1. All the states of the DEVS are in the admissible state set $S$. An execution of the model is to sequentially change its states, until ended explicitly. The change in its states is defined by two functions: internal transition function $\delta_{int}$ and external transition function $\delta_{ext}$.

Figure 1.8: Atomic DEVS state trajectory

$\delta_{int}:S\to S$ defines the autonomous internal behavior. The time when these changes take place is defined by function $ta:S\to R_{0,+\infty}^{+}$. It takes a state as a parameter and returns a non-negative real value denoting the time interval between state changes. The time for a DEVS is not discrete, because the simulation is not based on time-slicing. An internal transition can be scheduled at any point in the future on the real time-line (Figure 1.8).

An external event may occur at any time. $\delta_{ext}:Q\times X\to S$ is the external transition function. It defines which new state the DEVS should be changed to, when a certain external event is received. The new state depends on the old state and how long the DEVS has been in the old state (elapsed time). The old state $s$ and the elapsed time $e$ are usually represented as a tuple $(s,e)$, where $s\in S$ and $0 \leq e \leq ta(s)$.

Only internal transitions are allowed to produce output. $Y$ is the set of all possible output values. The output produced by a transition from the old state $s$ to any other state can be calculated with the $\lambda$ function. Value $\o$ means no output is produced.

All the input values are defined in $X$ and all the output values are defined in $Y$. They can be viewed as an interface exposed to the outside world. The outside world communicates with the Atomic DEVS only through input events and output events.