With the increasing number of devices performing Machine-Type Communications (MTC), mobile networks are expected to encounter a high load of burst transmissions. One bottleneck in such cases is the Random Access Channel (RACH) procedure, which is responsible for the attachment of devices, among other things. In this paper, we performed a rich-parameter based simulation on RACH to identify the procedure bottlenecks. A finding from the studied scenarios is that the Physical Downlink Control Channel (PDCCH) capacity for the grant allocation is the main limitation for the RACH capacity rather than the number of Physical Random Access Channel (PRACH) preambles. Guided by our simulation results, we proposed improvements to the RACH procedure and to PDCCH.