The Internet of Things (IoT) with its support for cyber-physical systems (CPS) will provide many latency-sensitive services that require very fast responses from network services. Mobile edge computing (MEC), one of the distributed computing models, is a promising component of the low-latency network architecture. In network architectures with MEC, mobile devices will offload heavy computing tasks to edge servers. There exist numbers of researches about low-latency network architecture with MEC. However, none of the existing researches simultaneously satisfy the followings: (1) guarantee the latency of computing tasks and (2) implement a real system. In this paper, we designed and implemented an MEC based network architecture that guarantees the latency of offloading tasks. More specifically, we first estimate the total latency including computing and communication ones at the centralized node called orchestrator. If the estimated value exceeds the latency requirement, the task will be rejected. We then evaluated its performance in terms of the blocking probability of the tasks. To analyze the results, we compared the performance between obtained from experiments and simulations. Based on the comparisons, we clarified that the computing latency estimation accuracy is a significant factor for this system.