The software‐defined networking (SDN) represents the future backbone of the Internet. In general, to understand the performance and the limitation of SDN is a prerequisite for deploying these networks and making the most of their resources. For achieving that goal, this paper discusses the difference between traditional networks and SDN over wide area network (WAN) where an accurate queuing model of packet forwarding is proposed to measure the performance of many factors affecting the system, such as response time, service rate, utilization, throughput and delay through a vEdge router. Additionally, it focusses for studying algebraic estimates of the probability distribution of the system states. The Matrix‐Geometric solution procedure of a phase‐type distribution queue with first‐in, first‐out (FIFO) discipline is used. The analysis results indicate that the proposed queuing model gives a more accurate approximation for software‐defined WAN (SD‐WAN) controller system performance than the present, where this solution shows that the most important results are benefits of centralized management of SD‐WAN, an increase in bandwidth through separating the control plan from the data plan, thus reducing volume operations in the data plan, a delay and an increase in packet transfer speed. Additionally, it improves business performance and diminishes budget.