## 2 Related Work  
Recently, there have been many works on how to enforce bandwidth guarantees in the cloud datacenter [17; 18; 19]. In accordance with the network characteristics of cloud datacenters, we classify these works into the following two categories: (1) In some studies such as Gatekeeper [20] and EyeQ [21], it is assumed that there is no congestion in the network core, and congestion only occurs in the endpoints of the server. Even though the path multiplicity technology (such as ECMP [22]) has been broadly used in the current datacenter, because of improper scheduling of VM flows, the problem of link congestion is still unsolved [11]. In addition, a central controller is employed for scheduling in [11], but scale-out is difficult to achieve. Thus, these solutions are impractical in reality. (2) In some other works, the authors do consider the possibility of congestion in the network core, such as SecondNet [13], Oktopus [14], Faircloud [15], Seawall [16], ElasticSwitch [23], NetShare [24; 25] and BwShare [26]. In [13; 14], the heuristic bandwidth allocation algorithms are designed and employed to map the virtual network to the physical network. In these two works, consideration was made to enforce the allocation of bandwidth, but they failed to consider work-conserving, and the utilization rate of underlying network is relatively low. In [15], the tradeoffs are achieved for sharing the resources of cloud networks based on various desirable properties and allocation policies. It manages to achieve both bandwidth guarantee and work conservation, but it also has some defects that cannot be ignored, and, for example, expensive hardware support and special network topology are required in order to implement bandwidth guarantee. In [16], by providing clear feedback from the receivers, traffic will be throttled at the sources before they use any network resources, which can prevent a malicious VM from hogging bandwidth in the network. This method is particularly efficient for the situation in which many VMs send traffic to one receiver, and compared to the case in which a VM of a different tenant on the same server with the same weight is receiving traffic from just one sender, it will occupy a significantly higher fraction of received bandwidth of the server link. This problem of unfairness is not solved in [23; 26] either. In [23], redundant capacity is shared among active VM-to-VM flows in proportion, but minimum bandwidth guarantee is provided due to the hypothesis that the virtual network is built on the hose model. Based on that, the excess bandwidth is allocated in a dynamic manner. The authors in [26] also enable transparent work conservation across all VMs, which allows VMs to reuse idled bandwidths across the cloud efficiently without hurting bandwidth guarantees. The authors in [24] ensure per-tenant fair sharing of congested links, and as more tenants use the link, the per-tenant sharing can be arbitrarily reduced. [PERSON] et al. [25] considered configurable fairness requirements of tenants, but the flow could be split into subflows.  
Compared to works mentioned above, our work focuses on the enforcement of VDC-based fair bandwidth guarantees. It can provide the minimum bandwidth guarantee based on our Switch Centered Graph (SCG) model, compatible with the hose model. Our method not only emphasizes providing bandwidth guarantees with work-conserving property, but also ensures the VDC-based fair allocation of resources.