In this paper, we consider a stationary model for the flow through a network. The flow is determined by the values at the boundary nodes of the network. We call these values the loads of the network. In the applications, the feasible loads must satisfy some box constraints. We analyze the structure of the set of feasible loads. Our analysis is motivated by gas pipeline flows, where the box constraints are pressure bounds.We present sufficient conditions that imply that the feasible set is star-shaped with respect to special points. Under stronger conditions, we prove the convexity of the set of feasible loads. All the results are given for passive networks with and without compressor stations.This analysis is motivated by the aim to use the spheric-radial decomposition for stochastic boundary data in this model. This paper can be used for simplifying the algorithmic use of the spheric-radial decomposition.

中文翻译：

---

固定流网络中可行集的凸性和星形

在本文中，我们考虑通过网络流动的平稳模型。流量由网络边界节点上的值确定。我们称这些值为网络负载。在应用中，可行载荷必须满足一些箱形约束。我们分析了可行载荷集的结构。我们的分析是受天然气管道流动的驱动，其中箱形约束为压力范围，我们提出了充分的条件，暗示可行集相对于特殊点是星形的。在更强的条件下，我们证明了可行载荷集的凸性。所有结果均针对具有和不具有压缩站的无源网络给出。本分析的目的是为了在此模型中将球体径向分解用于随机边界数据。