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 ρ is between load boundaries ρ₁

and ρ₂. 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. Further, we generalize the

results using a steady-state equilibrium based approach and develop

models for single-channel and multi-channel systems, incorporating the

barring probability PB. Ultimately, we identify the de-correlating

effect of parameters O, PB, and T_omax and introduce the

Poissonization effect due to the backlogged requests in a slot. We

investigate the impact of Poissonization on different traffic and

conclude this thesis.