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Machine type communications (MTC) in 3G/4G networks is getting more attentionrecently due to bursty nature of traffic characteristics in contrast to Poissontype H2H traffic. A large number of methods have been suggested in theliterature. In this paper we give a mathematical model on performance analysisof Disjoint Allocation (DA) and Joint Allocation (JA) methods for allocatingpreambles to M2M and H2H users. In an earlier work we had investigated theperformance of two possible splitting preamble methods on collision probabilityand energy reduction for MTC subscribers. In this paper we develop a stochasticmodel for JA/DA method in RACH procedure using a $K$th order Markov chainapproach and carry out performance analysis in terms of collision probability,access success probability, average access delay, statistics of preambletransmissions and statistics of access delay for M2M users. The optimal numberof reserved preamble set is derived based on the given success access delaythreshold. Numerical results verifies the simulation results and demonstratesthat this model can estimate the performance of the JA/DA method accurately.

Performance Analysis of Split Preamble RAN Over-load Protocol for M2M Communications in Cellular Networks