## 1 Introduction  
The fifth-generation (5G) communications systems are facing the challenge to support a wide range of industrial applications [1] such as mobile broadband and massive machine type communications, mission-critical applications as well as traditional voice and data. Table 1 summarizes typical examples and performance requirements for 5G use cases ranging from general broadband access with global coverage or ultra-low latency services to dedicated networks for the Internet of things (IoT) or extreme mobility [2]. Obviously, a single network structure cannot afford the differentiated requirements among these applications simultaneously. To handle such diversity, building a service-specific network infrastructure for each case is a straightforward solution [3]. However, the significant operational and capital expenditures and maintenance complexity are unaffordable for telecom operators. The concept of network slicing (NS) [1] is considered as an efficient solution to address the diverse requirements of applications in 5G networks. By slicing a single physical substrate network, multiple end-to-end (E2E) logical networks are tailored for operators to provide corresponding services in parallel, where the NS is mutually isolated, managed independently and created on demand. Each logical slice corresponds to an abstraction of a subset of physical substrate network resources, aiming to logically separate the set of virtual network functions (VNFs) within the physical infrastructure. For example, one network slice is dedicated to augmented reality applications with ultra-reliable and low-latency communications, whereas another slice is designated for extremely high throughput video-on-demand services. With the powerful software-defined networking (SDN) and network function virtualization (NFV) technologies available, NS can be centrally managed and fast deployed with better resource utilization and cost efficiency according to the requirement of each use case [4]. With NFV, it would be possible to flexibly tailor the slice for a specific scenario, while SDN controller is acknowledged as an enabler to remotely configure the physical network. Although the topic of enabling technologies, SDN and NFV, are well investigated for many slice realization models, the extension to the characteristics of NS (i.e., the topology, required virtual functions and interconnections) is not straightforward [5; 6]. In order to provide efficient and practical deployment policies for E2E slices in the backhaul transport network, it is of major significance to construct the logical NS model, substrate network model, and resource mapping relationships. In the logical network, each NS can be interpreted as an E2E traffic flow with multiple communication service instances to support specific and extreme performances in terms of latency, throughput, capacity and availability. Each communication service instance is composed of a sequence of virtual network units (VNUs) and virtual links, which can be illustrated as a service chain (SC). VNUs which carry dedicated VNFs (e.g., BBUs (Building Baseband Units), GWs (Gateways) or MMEs (Mobility Management Entities)) can be deployed onto network data centers (DCs) and run on the general-purpose hardware. A virtual link between VNUs can be realized as a multi-hop physical path. Hence, the NS resource allocation can be defined as a feasible path that slice traffic should follow in infrastructure networks with adequate resource availability. In other words, the realization of NS, in essence, is to deploy VNUs and virtual links into physical communications infrastructures. There are plentiful related researches on VNFs deployment and virtual network embedding [7; 8], bringing constructiveness in evolving NS resource allocation schemes. However, little work has been done on allocating substrate resources to virtual networks \"on demand\" within the backhaul.