In 2001, D. Erwin \cite{Erw01} introduced in his Ph.D. dissertation the notion of broadcast independence in unoriented graphs. Since then, some results but not many, are published on this notion, including research work on the broadcast independence number of unoriented circulant graphs \cite{LBS23}. In this paper, we are focused in the same parameter but of the class of oriented circulant graphs. An independent broadcast on an oriented graph $\overrightarrow{G}$ is a function $f: V\longrightarrow \{0,\ldots,\diam(\overrightarrow{G})\}$ such that $(i)$ $f(v)\leq e(v)$ for every vertex $v\in V(\overrightarrow{G})$, where $\diam(\overrightarrow{G})$ denotes the diameter of $\overrightarrow{G}$ and $e(v)$ the eccentricity of vertex $v$, and $(ii)$ $d_{\overrightarrow{G}}(u,v) > f(u)$ for every distinct vertices $u$, $v$ with $f(u)$, $f(v)>0$, where $d_{\overrightarrow{G}}(u,v)$ denotes the length of a shortest oriented path from $u$ to $v$. The broadcast independence number $\beta_b(\overrightarrow{G})$ of $\overrightarrow{G}$ is then the maximum value of $\sum_{v \in V} f(v)$, taken over all independent broadcasts on $\overrightarrow{G}$. The goal of this paper is to study the properties of independent broadcasts of oriented circulant graphs $\overrightarrow{C}(n;1,a)$, for any integers $n$ and $a$ with $n>|a|\geq 1$ and $a \notin \{1,n-1\}$. Then, we give some bounds and some exact values for the number $\beta_b(\overrightarrow{C}(n;1,a))$.

翻译：2001年，D. Erwin \cite{Erw01}在其博士论文中首次提出了无向图中广播独立性的概念。此后，关于该概念的研究成果虽有发表但数量有限，其中包括无向循环图广播独立数的研究工作\cite{LBS23}。本文聚焦于同一参数，但研究对象为定向循环图类。定向图$\overrightarrow{G}$上的独立广播是一个函数$f: V\longrightarrow \{0,\ldots,\diam(\overrightarrow{G})\}$，满足$(i)$ 对每个顶点$v\in V(\overrightarrow{G})$有$f(v)\leq e(v)$，其中$\diam(\overrightarrow{G})$表示$\overrightarrow{G}$的直径，$e(v)$表示顶点$v$的离心率；且$(ii)$ 对任意满足$f(u), f(v)>0$的不同顶点$u$、$v$有$d_{\overrightarrow{G}}(u,v) > f(u)$，其中$d_{\overrightarrow{G}}(u,v)$表示从$u$到$v$的最短定向路径长度。则$\overrightarrow{G}$的广播独立数$\beta_b(\overrightarrow{G})$定义为所有独立广播上$\sum_{v \in V} f(v)$的最大值。本文旨在研究定向循环图$\overrightarrow{C}(n;1,a)$（其中$n$和$a$为整数，满足$n>|a|\geq 1$且$a \notin \{1,n-1\}$）的独立广播性质。进而，我们给出了参数$\beta_b(\overrightarrow{C}(n;1,a))$的若干界和精确值。