# Link Load Correlation-Based Blocking Performance Analysis for Tree-Type Data Center Networks
###### Abstract  
With the explosive growth of cloud computing applications, the east-west traffic among servers has come to occupy the dominant proportion of the traffic in data center networks (DCNs). Cloud computing tasks need to be executed in a distributed manner on multiple servers, which exchange large amounts of intermediate data between the adjacent stages of each multi-stage task. Therefore, the congestion in DCNs can reduce the processing performance when conducting multi-stage tasks. To address this, the relationship between the blocking performance and the traffic load can be adopted as a theoretical basis for network planning and traffic engineering. In this paper, the traffic load correlation between edge links and aggregation links is considered, and an iterative blocking performance analysis method is proposed for two-layer tree-type DCNs. The simulation results show the good accuracy of the proposed method with respect to the theoretical results especially in the blocking rate range below 4% and with over-subscription ratio 1.5.  
data center networks; network blocking probability; network performance analysis; load correlation +
Footnote †: journal: Applied  
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computing applications, in terms of computing and network resources. To improve their revenue-cost ratio while guaranteeing the QoS of applications at the same time, the SP should determine the allowable traffic load level and optimize the cloud computing task placements, according to the network configuration provided by the InP; meanwhile, the InP should design the network deployment and upgrade solutions on the basis of the traffic intensity provided by the SP. In this case, the relationship between the blocking performance and the traffic load acts as an important basis for network plan and task placement in cloud data centers. In the beginning, blocking probability is defined as the statistical probability that a telephone connection cannot be established due to insufficient transmission resources in the network [8]. Later, blocking probability also applies to end-to-end connections or flows including a sequence of packets sharing the same five-tuple [9]. In the circuit switching networks or connection-oriented packet switching networks, a blocking means a call or connection cannot be established; while in the general connectionless mode transmission, if some packets are blocked, they may be temporarily stored in the buffer waiting for idle bandwidth or may be discarded if the buffer is full or timeout expires [10]. Thus, though there may be no actual blockings for the whole data flow, the blocking probability performance is also related to other QoS indicators such as delay and packet-loss ratio and can still act as an implicit network performance metric in packet switching networks. Network blocking performance analysis can be traced back to computing the blocking probabilities of circuit switching networks. [PERSON] of the Bell Laboratories first considered analyzing the blocking rate of circuit switching networks with single-channel links [11]. Assuming that the loads of different links are independent, the blocking rate of a multi-stage circuit switching network can be obtained. Based on the link load independence assumption, the theoretical blocking rate obtained by [PERSON]'s method is higher than that of the simulation result and, therefore, can be used as a conservative upper bound for the network blocking probability. [PERSON] took into account the load correlation of the front and rear links in the crossbar circuit switching network, and derived the theoretical lower bound for the blocking probability [12]. [PERSON] extended [PERSON]'s and [PERSON]'s blocking analysis models to multi-rate networks, such as asynchronous transfer mode (ATM) circuit switching networks and packet-switched networks [13], where the rate of each link can be continuous or discrete. Besides multi-stage circuit switching networks, the blocking performance of optical switching networks has also been widely discussed.