With the increasing number of Internet of Things (IoT) devices, Machine Type Communication (MTC) has become an important use case of the Fifth Generation (5G) communication systems. Since MTC devices are mostly disconnected from Base Station (BS) for power saving, random access procedure is required for devices to transmit data. If many devices try random access simultaneously, preamble collision problem occurs, thus causing latency increase. In an environment where delay-sensitive and delay-tolerant devices coexist, the contention-based random access procedure cannot satisfy latency requirements of delay-sensitive devices. Therefore, we propose RAPID, a novel random access procedure, which is completed through two message exchanges for the delay-sensitive devices. We also develop Access Pattern Analyzer (APA), which estimates traffic characteristics of MTC devices. When UEs, performing RAPID and contention-based random access, coexist, it is important to determine a value which is the number of preambles forRAPID to reduce random access load. Thus, we analyze random access load using a Markov chain model to obtain the optimal number of preambles for RAPID. Simulation results show RAPID achieves 99.999% reliability with 80.8% shorter uplink latency, and also decreases random access load by 30.5% compared with state-of-the-art techniques.