Software-Defined Networking (SDN) shows us a promising picture to deploy the demanding services in a fast and cost-effective way. Till now, most SDN use cases are deployed in enterprise/campus networks and data center networks. However, when applying SDN to the large-scale networks, such as Wide Area Network (WAN), the end-to-end delay of packet traversal is suspected to be very large and needs to be further investigated. Moreover, stringent time constraint is the cornerstone for real-time applications in SDN. Understanding the packet delay in SDN-based large networks is crucial for the proper design of switch architecture and the optimization of network algorithms such as flow control algorithms. In this paper, we present a thorough systematic exploration on the end-to-end delay in SDN which consists of multiple nodes, fully exposing the components which contribute to the long delay. We disclose that SDN switches cannot completely avoid the generation of flow setup even in proactive mode and conduct data mining on the probability of flow setup. We propose an analytical model for the end-to-end delay. This model takes into account the impact of the different rule installation time consumption on different switches. Considering the delay in switches contributes a large proportion to the entire delay, we conduct various measurements on the delay of a single switch. Results for the delay at different flow setup rates and with different rule priority patterns are presented. Furthermore, we study the impact on packet delay caused by ternary content addressable memory (TCAM) update. We measure parameters in the delay model and find that if SDN is deployed in all segments of WAN, the delay of packet traversal will be increased up to 27.95 times in the worst case in our experimental settings, compared with the delay in conventional network. Such high delay may eventually lead the end-to-end connections fail to complete if no additional measures are taken.