  LTE random access procedure performs satisfactorily in case of asynchronous,
uncorrelated traffic arrivals. However, when the arrivals are correlated and
arrive synchronously, the performance of the random access channel (RACH) is
drastically reduced, causing a large number of devices to experience outage. In
this work we propose a LTE RACH scheme tailored for delay-sensitive M2M
services with synchronous traffic arrivals. The key idea is, upon detection of
a RACH overload, to apply a collision resolution algorithm based on splitting
trees. The solution is implemented on top of the existing LTE RACH mechanism,
requiring only minor modifications of the protocol operation and not incurring
any changes to the physical layer. The results are very promising,
outperforming the related solutions by a wide margin. As an illustration, the
proposed scheme can resolve 30k devices with an average of 5 preamble
transmissions and delay of 1.2 seconds, under a realistic probability of
transmissions error both in the downlink and in the uplink.
