## 1 Introduction
The \"on demand\" implies that VNUs are mapped into the appropriate DCs according to the amount of slice traffic and desired performance requirements to avoid poor quality of service (QoS) and user experience, load imbalance of physical network, and low-cost efficiency of operators. Since ultra-low latency is a critical performance of some 5G services in data transmission, networks with extreme QoS demands become the beneficiaries of network slicing [9]. In critical applications, including autonomous driving and mechanical arms, the requirements for latency could be extremely stringent. Meanwhile, both Huawei and Vodafone have pointed out that low latency is also a key \begin{table}
\begin{tabular}{c c c} \hline \hline
**Cases** & **Applications** & **Requirements** \\ \hline Enhanced mobile broadband access in dense areas (eMBB) & Hologram, high-definition (HD) video, user mobile broadband in a stadium & High traffic volume, high throughput \\ \hline Small-volume, critical communications (s-VCC) & Robotic control, industry control & High reliability, ms latency, small traffic volume \\ \hline High-volume, critical communications (h-VCC) & e-Health, virtual reality (VR) & High reliability, ms latency, high traffic volume \\ \hline Extreme real-time communications (eRTC) & Autonomous driving, driving assistant, automotive factory & Sub-ms latency, mobility, high traffic volume \\ \hline Massive Internet of Things (mIoT) & Smart wearables, meters, sensors & Massive connection, low power \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key 5G use cases and their requirements. metric to improve the user experience of mobile wide-band services, e.g., VR of 5G eMBB. On the other hand, for instance, E2E latency reduction may promote reliability as well, as the service's traffic can be steered through additional redundant VNFs [10]. Furthermore, the network state and requested traffic are time-varying, whose future information is hard to learn in advance. Reducing the transport network latency is necessary for preventing the extreme QoS from deteriorating due to the poor network state and unexpected traffic. The optimal-latency resource allocation in backhaul transport networks deserves more attention; however, the related research of NS is still nascent. Although the deployment of E2E NS has been studied in several institutions, little work in the existing literature has been done on the latency-optimal slicing, whose studies on latency are merely subject to latency constraints, as highlighted in [11]. Actually, the latency can be heavily deteriorated due to many factors. The efficient deployment policy for E2E slices is difficult to determine, which should assess allocation priorities of network infrastructures according to service requirements and network features. For example, the DC in core layer network owns more powerful capability, which should be assigned a high priority to deal with the mass of HD video services rather than latency-sensitive ones, due to the farther physical location. The aforementioned problems motivate us to address the latency-optimal VNF resource allocation problem in the backhaul transport network. According to the small-world and scale-free topological properties of many real-life communications networks [12; 13], our model analyzes NS topological characteristics, physical network features, and mapping relationships. We then formulate the problem as an integer linear programming (ILP), jointly taking into account slice requirements and network structural characteristics. The problem is solved with the branch-and-bound algorithm to yield the optimal physical path that the slice traffic follows on demand. Numerical results verify that our proposed model can find out the latency-optimal VNUs and virtual links mapping. With comparison to Robust Network Slice Design Problem (NSDP) [14] and Random Fit Placement Algorithm (RFPA) [15], our scheme can optimize the transport network latency and improve load-balance and serviceability.