GSM networks consist of cells that can support mobile users. Due to this mobility, it is expected that the network model can be different than that of wired networks which do not support mobile users. In our study, using empirical data provided by a GSM operator, TURKCELL, we analyze the associated network model from the mobility perspective. We first show that the handover rate of a regular cell is not negligible. Therefore, call arrivals (answered calls or new calls) in a cell have to be modeled by taking into account the handover calls, which terminate in a different cell than it originated from. However in the related literature this handover rate is usually ignored. We demonstrate that the call arrivals of both handover calls, and inner calls (which terminate in the originated cell) can be separately modeled as Poisson variables with unity fraction of variance and mean by using chi-square test evaluation. We use Wavelet Transformation (WT), autocorrelation function and Modified Allan Variance (MAVAR) methods to investigate the correlation between call arrivals to indicate the relevance of Poisson model. We show that call arrivals in a second is found perfectly uncorrelated with call arrivals in other seconds and Poisson distributed for both mobile and fixed cases regardless the time of the day. The result presented here are useful to evaluate performance of GSM network and to utilize network resources efficiently.