Operators of reconfigurable wavelength-division multiplexed (WDM) optical networks adapt the lightpath topology to balance load and reduce transmission delays. Such an adaption generally depends on a known or estimated traffic matrix. Network function virtualization (NFV) allows to implicitly change this traffic matrix. However, these two degrees of freedom have largely been considered separately, using resources suboptimally. Especially for delay-sensitive services, an optimal use of resources can be crucial. We aim to jointly optimize the embedding of virtualized network function (VNF) forwarding graphs with delay constraints and the lightpath topology of WDM optical networks. Unlike previous work, we consider all three types of delays: propagation, processing and forwarding-induced queuing delay. We model the latter two as M/M/1 queues. We formulate and analyze a mixed-integer nonlinear program (MINLP), reformulate it as a mixed-integer quadratic constrained program (MIQCP) and approximate it by a mixed-integer linear program (MILP). We evaluate our approach for small-scale examples of a multicast service.

翻译：可重构波分复用（WDM）光网络的运营商通过调整光路拓扑来均衡负载并降低传输延迟。这种调整通常依赖于已知或估计的流量矩阵。网络功能虚拟化（NFV）能够隐式地改变该流量矩阵。然而，这两种自由度在很大程度上被独立考虑，导致资源利用不充分。特别是对于延迟敏感型服务，资源的最优利用至关重要。本文旨在联合优化具有延迟约束的虚拟化网络功能（VNF）转发图的嵌入与WDM光网络的光路拓扑。与先前工作不同，我们考虑了所有三种延迟类型：传播延迟、处理延迟以及转发引起的排队延迟。我们将后两种延迟建模为M/M/1队列。我们提出并分析了一个混合整数非线性规划（MINLP），将其重构为混合整数二次约束规划（MIQCP），并通过混合整数线性规划（MILP）进行近似。我们针对一个多播服务的小规模实例评估了所提方法。