  The advent of Machine-to-Machine communication has sparked a new wave of
interest to random access protocols, especially in application to LTE Random
Access (RA). By analogy with classical slotted ALOHA, state-of-the-art models
LTE RA as a multi-channel slotted ALOHA. In this letter, we direct the
attention to the resource consumption of RA. We show that the consumption is a
random variable dependent on the contention parameters. We consider two
approaches to include the consumption into RA optimization: by defining
resource efficiency and by the means of a bi-objective optimization, where
resource consumption and throughput are the competing objectives. We then
develop the algorithm to obtain Pareto-optimal RA configuration under resource
constraint. We show that the algorithm achieves lower burst resolution delay
and higher throughput than the state-of-the-art.
