Handling congestion in LTE/5G cellular networks has become a critical issue due to recent, rapid increase in cellular network traffic. Control plane congestion becomes particularly serious when accommodating massive M2M/IoT terminals into cellular networks. Although various methods have been proposed for accommodation of M2M/IoT terminals, most of them are mainly based on mathematical analysis and simulation experiments. In this paper, we show the experimental evaluation results of the performance of a mobile core network to assess the impact of bursty access from M2M/IoT terminals. First, we constructed our experimental environment based on open-source implementation of mobile core networks and emulated user terminals. Then, we conducted experiments on simultaneous attach requests from multiple user terminals and measured the processing delay at each mobile core node. The results of our evaluations proved that concentrating attach requests from forty user terminals increases the processing time at a mobility management entity (MME) by up to around 510% when an MME node is operated on a virtual machine with 1 GHz / 1 core CPU.