We present a queuing system with elastic and inelastic jobs for the analysis of the joint transmission of traffic from machine-type and broadband communications in an LTE cell. The elastic jobs arriving in the system form a Markovian Arrival Process and are serviced according to the discipline of egalitarian processor sharing on the resources allocated by blocks. We obtain a system of equilibrium equations for calculating the stationary probability distribution of states and expressing the main performance characteristics. Using the example of the system under consideration, we investigate the relationship between system performance characteristics and the correlation coefficient of consecutive intervals between arrivals in the Markovian Arrival Process.