User:Cbogart2

Deterministic DEVS and Non-deterministic DEVS

Let ${\displaystyle A}$ and ${\displaystyle B}$ be two arbitrary sets. Then function ${\displaystyle f:A\rightarrow B}$ is called deterministic if give an ${\displaystyle a\in A}$, the values of callings ${\displaystyle f(a)}$ at different times are identical. Otherwise, ${\displaystyle f}$ is called non-deterministic.

A DEVS ${\displaystyle M=<X,Y,S,ta,\delta _{ext},\delta _{int},\lambda >}$ is called deterministic if ${\displaystyle ta}$, ${\displaystyle \delta _{ext}}$, ${\displaystyle \delta _{int}}$ and ${\displaystyle \lambda }$ are deterministic. Otherwise, ${\displaystyle M}$ is called non-deterministic.

The atomic DEVS Model for Ping-Pong Players

The atomic DEVS model for player A of Fig. 1 is given Player=${\displaystyle <X,Y,S,s_{0},ta,\delta _{ext},\delta _{int},\lambda >}$ such that

${\displaystyle X=\{?receive\}\,}$

${\displaystyle Y=\{!send\}\,}$

${\displaystyle S=\{(d,\sigma )|d\in \{Wait,Send\},\sigma \in \mathbb {T} ^{\infty }\}\,}$ and ${\displaystyle s_{0}=(Send,0.1)\,}$

${\displaystyle ta(s)=\sigma {\text{ for all }}s\in S\,}$

${\displaystyle \delta _{ext}((Wait,\sigma ),t_{e}),?receive)=(Send,0.1)\,}$

${\displaystyle \delta _{ext}((Send,\sigma ,t_{e}),?receive)=(Send,\sigma -t_{e})\,}$

${\displaystyle \delta _{int}(Send,\sigma )=(Wait,\infty ),\delta _{int}(Wait,\sigma )=(Send,0.1)\,}$

${\displaystyle \lambda (Send,\sigma )=?send,\lambda _{int}(Wait,\sigma )=\phi \,}$

Both of Player A and Player B are deterministic DEVS models.