The paper address resource allocation in an LTE call with both human-to-human and machine-to-machine (M2M) communications. M2M aggregation and access barring are considered as a means to reduce congestion due to the nature of M2M traffic. The cell is modelled as a multiservice queueing system with streaming and elastic customers. Resources for M2M communications are allocated in batches of fixed size; requests for them arrive according to a Markovian arrival process. We obtain the stationary probability distribution of the system and formulas for its performance measures and propose an algorithm for their computation. © 2017, Springer International Publishing AG.