LTE-Advanced networks employ random access based on preambles transmitted according to multi-channel slotted Aloha principles. The random access is controlled through a limit W on the number of transmission attempts and a timeout period for uniform backoff after a collision. We model the LTE-Advanced random access system by formulating the equilibrium condition for the ratio of the number of requests successful within the permitted number of transmission attempts to those successful in one attempt.

We prove that for W ≤ 8 there is only one equilibrium operating point and for W ≥ 9 there are three operating points if the request load p is between load boundaries p₁ and p₂. We analytically identify these load boundaries as well as the corresponding system operating points. We analyze the throughput and delay of successful requests at the operating points and validate the analytical results through simulations.