With the rise of the user base of smartphones, the cellular networks are facing increasing uplink signalling traffic pressure caused mainly by the soaring background traffic of smartphone applications. Therefore, this paper studies the LTE radio resource control (RRC) state transition, which is highly related to the amount of signalling traffic, caused by the background traffic. Firstly, we propose a general method for generating the background traffic using a burst model, taking the Gtalk as an example. Secondly, a novel theoretical model is proposed to calculate the number of RRC state transition, the probability of a smartphone's being in RRC CONNECTED and the distribution of the number of smartphones in RRC CONNECTED at a given epoch, all of which are key metrics for the cellular networks. Finally, both theoretical and simulation results are compared for a typical LTE macro cell scenario containing 300 cell phones, 80% of which are smartphones. The study also shows that the Gaussian distribution, which turns out to be a very good approximation, can be used to fit the distribution of the instantaneous number of smartphones in RRC CONNECTED in a LTE cell.
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