  Random Access Channel (RACH) has been identified as one of the major
bottlenecks for accommodating massive number of machine-to-machine (M2M) users
in LTE networks, especially for the case of burst arrival of connection
requests. As a consequence, the burst resolution problem has sparked a large
number of works in the area, analyzing and optimizing the average performance
of RACH. However, the understanding of what are the probabilistic performance
limits of RACH is still missing. To address this limitation, in the paper, we
investigate the reliability of RACH with access class barring (ACB). We model
RACH as a queuing system, and apply stochastic network calculus to derive
probabilistic performance bounds for burst resolution time, i.e., the worst
case time it takes to connect a burst of M2M devices to the base station. We
illustrate the accuracy of the proposed methodology and its potential
applications in performance assessment and system dimensioning.
