With the emergence of compute-intensive applications and rapid growth of mobile users and Internet of Things(IoT) devices, edge computing was proposed to provide cloud-like services in close proximity to meet the requirements of low-latency, security, and lower energy consumption. Ultra-dense network (UDN) is a promising technique to meet the requirements of explosive data traffic in 5G mobile communications to improve regional spectrum efficiency and network coverage. This paper proposed an optimal deployment and allocation strategy for deploying edge servers(ESs) in UDN to minimize the cost of service providers and to guarantee the completion time of services. Based on queuing theory and vector quantization(VQ) technique, the strategy can optimize both the number and locations of edge servers, and mobile users allocation for the given UDN environments. The experimental results show that the strategy is superior to existing algorithms in both qualitative and quantitative aspects, and can minimize the cost of deployment and guarantee the mobile user's requirements for the completion time of the offloading task.