Abstract-The development of Machine-Type Communication (MTC) in the Long Term Evolution (LTE) standard can lead to an overuse of the Physical Random Access Channel (PRACH). An efficient way to avoid it consists in reducing the number of requests done by end-devices. In this paper, we first study the probability of collision in a congested LTE-MTC network. As a second step, we analyze the latency in the network as a function of the request access rate. Then, we propose a closed-form for a sub-optimal request access rate. We finally conduct numerical simulations in order to assess the performance of the proposed approximation.