Modeling RACH Arrivals and Collisions for Human-Type Communication

This letter proposes an analytical model to evaluate the collision probability on the Random-Access CHannel (RACH) in Long-Term Evolution systems as a function of the number of user equipment, the number of available preambles, and the Inter-arrival times of the RACH Requests (IRRs) of the average user. The model for the IRR of the average user is obtained from real traffic data captured at the eNodeB of a mobile operator, and is derived by emulating the radio resource control (RRC) state machine for different RRCs Inactivity timer (RRCIT) settings. The results of this letter suggest that when RRCIT is set to a few seconds, a mixture model is more accurate than the Poisson hypothesis both in modeling the IRR and in estimating the RACH performance.