Slices were introduced in 5G to enable the co-existence of applications with different requirements on a single infrastructure. Slices may be delay-constrained for mission-critical applications such as Tactile Internet applications. When delay-constrained slices are implemented as collections of virtual network function (VNF) chains, a key challenge is to place the VNFs and route the traffic through the chains to meet a strict delay constraint. Parallel VNF processing has been proposed as a promising approach. However, this approach increases the number of physical nodes in the chains, and thus decreases the reliability, which is also critical for Tactile Internet applications. Furthermore, the cost depends upon the specific VNF placement and traffic routing, as nodes and links are heterogeneous. This article tackles the issues of reliability and cost when embedding delay-constrained slices. We model the problem as an optimization problem that minimizes reliability degradation and cost while ensuring the strict delay constraint when a parallel VNF processing approach is used. Due to the complexity of the formulated problem, we also propose a Tabu search-based algorithm to find sub-optimal solutions. The results indicate that our proposed algorithm can significantly improve cost and reliability while meeting a strict delay constraint.

中文翻译：

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使用并行 VNF 处理方法嵌入延迟约束切片时确保可靠性和低成本

5G 中引入了切片，以支持具有不同要求的应用程序在单个基础设施上共存。对于关键任务应用程序（例如触觉互联网应用程序），切片可能会受到延迟限制。当延迟受限切片被实现为虚拟网络功能 (VNF) 链的集合时，一个关键挑战是放置 VNF 并通过链路由流量以满足严格的延迟约束。已提出并行 VNF 处理作为一种有前途的方法。然而，这种方法增加了链中物理节点的数量，从而降低了可靠性，这对于触觉互联网应用来说也是至关重要的。此外，成本取决于特定的 VNF 布局和流量路由，因为节点和链接是异构的。本文解决了嵌入延迟受限切片时的可靠性和成本问题。我们将问题建模为一个优化问题，在使用并行 VNF 处理方法时，最大限度地减少可靠性下降和成本，同时确保严格的延迟约束。由于公式化问题的复杂性，我们还提出了一种基于禁忌搜索的算法来寻找次优解。结果表明，我们提出的算法可以显着提高成本和可靠性，同时满足严格的延迟约束。我们还提出了一种基于禁忌搜索的算法来寻找次优解决方案。结果表明，我们提出的算法可以显着提高成本和可靠性，同时满足严格的延迟约束。我们还提出了一种基于禁忌搜索的算法来寻找次优解决方案。结果表明，我们提出的算法可以显着提高成本和可靠性，同时满足严格的延迟约束。