Joint scheduling and routing of data flows with deadline constraints in communication networks has been attracting research interest. This type of problem distinguishes from conventional multicommodity flows due to the presence of the time dimension. In this paper, we address a flow routing and scheduling problem with delivery deadline, where the assignment of link capacity occurs in discrete units. Discrete capacity allocation is motivated by applications in communication systems, where it is common to have a base unit of capacity (e.g., wavelength channel in optical communications). We present and prove complexity results of the problem. Next, we give an optimization formulation based on a time slicing approach (TSA), which amounts to a discretization of the time into time slices to enable to formulate the deadline constraints. We then derive an effective reformulation of the problem, via which a column generation algorithm (CGA) is developed. In addition, we propose a simple and fast Max-Flow based Algorithm (MFA). We use a number of network and traffic scenarios to study various performance aspects of the algorithms.

中文翻译：

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具有期限和离散容量分配的网络流的路由和调度

通信网络中具有截止日期约束的数据流的联合调度和路由已经引起了研究兴趣。由于时间维度的存在，这类问题与传统的多商品流不同。在本文中，我们解决了具有交付期限的流路由和调度问题，其中链路容量的分配发生在离散单元中。离散容量分配的动机是在通信系统中的应用，其中通常具有容量的基本单位（例如，光通信中的波长信道）。我们提出并证明问题的复杂性结果。接下来，我们给出了基于时间切片方法 (TSA) 的优化公式，这相当于将时间离散化为时间片，以便制定截止日期约束。然后我们推导出问题的有效重构，通过它开发了列生成算法 (CGA)。此外，我们提出了一种简单快速的基于最大流量的算法（MFA）。我们使用许多网络和流量场景来研究算法的各个性能方面。