The goal of Network Function Virtualization (NFV) is to build agile and service-aware networks by building a new paradigm of provisioning network services where physical network functions are deployed as Virtualized Network Functions (VNFs). Due to the advantages of NFV, 5G networks have adopted NFV as one of its key enabling technologies. One of the most important challenges for realizing NFV-enable 5G Networks is VNF placing and routing. However, most existing studies neglected flow rate fluctuation of service requests, which could cause service migration and fluctuation of queues (buffers) in the networks. In this paper, we study the cost-minimizing problem of VNF placing and routing in this dynamic environment while considering service migration and queue backlog stability. We first formulate the problem as a stochastic optimization problem. Then we propose an online algorithm, named MACRO, to solve the problem. In order to bound the worst-case delay encountered by requests we propose WEB-MACRO. MACRO and WEB-MACRO base on Lyapunov optimization and make decisions without knowing future information. The theoretical analysis suggests that MACRO and WEB-MACRO achieve an optimality gap of $\mathcal{O}\left(\frac{1}{\mathcal{V}}\right)$, where $\mathcal{V}$ is a tunable parameter that controls the tradeoff between cost and backlogs. In addition, the queue backlogs maintained by MACRO are bounded by $\mathcal{O}\left(\mathcal{V}\right)$ and the queue backlogs maintained by WEB-MACRO are upper bounded which accordingly bounds the worst-case delay encountered by service requests. The experiment results suggest that MACRO and WEB-MACRO achieve queue stability and reduce the total cost by 36.49% when $\mathcal{V}=2$ and 45.84% when $\mathcal{V}=6$, compared with the state-of-the-art method.

网络功能虚拟化（NFV）的目标是通过建立新的供应网络服务范式来构建敏捷和可感知服务的网络，其中将物理网络功能部署为虚拟化网络功能（VNF）。由于NFV的优势，5G网络已将NFV用作其关键启用技术之一。实现启用NFV的5G网络的最重要挑战之一是VNF的放置和路由。但是，大多数现有研究都忽略了服务请求的流量波动，这可能会导致服务迁移和网络中队列（缓冲区）的波动。在本文中，我们在考虑服务迁移和队列积压稳定性的同时，研究了在这种动态环境中VNF放置和路由的成本最小化问题。我们首先将该问题表述为随机优化问题。然后，我们提出了一种名为MACRO的在线算法来解决该问题。为了限制请求遇到的最坏情况的延迟，我们建议使用WEB-MACRO。MACRO和WEB-MACRO基于Lyapunov优化，并且在不了解未来信息的情况下做出决策。理论分析表明，MACRO和WEB-MACRO达到了最优的差距$\mathcal{Ø}（\frac{\mathrm{1个}}{\mathcal{伏特}}）$， 在哪里 $\mathcal{伏特}$是一个可调参数，用于控制成本与积压之间的权衡。此外，由MACRO维护的队列积压工作受到以下限制：$\mathcal{Ø}（\mathcal{伏特}）$WEB-MACRO维护的队列积压是上限，因此限制了服务请求遇到的最坏情况的延迟。实验结果表明，MACRO和WEB-MACRO可以实现队列稳定性，并且在总成本降低36.49％时，$\mathcal{伏特}=\mathrm{2个}$ 和45.84％ $\mathcal{伏特}=6$与最先进的方法相比。