For the Internet of things, having sensors in devices used for video surveillance services, such as cameras, is crucial. The advancement of edge computing technology has enabled high computing capacity and the handling of massive data sets. The concept of cloudlets is employed in edge computing for in-network processing, especially for large-size multimedia data processing. Cloudlets are essential for services with high computing costs. Contrary to traditional cloud computing, data can be offloaded to in-network devices and core clouds, thereby improving the quality of service and enhancing resource utilization. However, the trade-off between network transmissions and nodal processes with delay-aware multimedia traffic has been demonstrated to be an NP-complete problem. The problem is presented as a mathematical formula to maximize the minimal delay gap between the tolerable event delay, sending time, and processing time. The problem is subject to in-network processing node assignment, routing paths, transmission capacities, computing capacities, and the effective service period. The Lagrangian approach was employed to evaluate the method proposed in this study; a near-optimal solution was obtained, and several experiments were performed to demonstrate that the proposed method outperforms existing methods.