Traffic management based on video data captured by CCTV cameras causes a permanent stress on the network paths to the traffic monitoring centers. The recently introduced paradigm of edge computing can reduce the communications bandwidth requirement between the TMC and cameras by installing the computing resources, e.g., cloudlets, nearby the cameras. However, the cloudlets are designed as resource-poor facilities owing to scalability and economical deployment issues, and thus, the video processing capabilities at the cloudlets are limited. In this paper, we focus on the traffic detection problem and propose a two-tier edge computing based model that takes into account of both the computing capability of the TMC and the low bandwidth requirement of the cloudlets. To this end, we develop a traffic detection algorithm with two configurations; one designed based on the cloudlets' computing capability, and the other one with high accuracy to be executed at the TMC. Moreover, the performance of the proposed two-tier model as well as the traffic detection algorithm is evaluated via test-bed experiments in which we show the traffic detection accuracy can be maximized by switching between the video processing at the edge and the cloud.