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Residence times relationships in wireless communication systems with differentiated quality zones

Different cellular systems with different resource management strategies have similar residence time characterization due to geometrical similarities. In such systems, different quality zones, in terms of the signal-to-interference ratio, are distinguished inside each cell. In this paper, the functional relationship between the cell residence time and the residence time in the different quality zones is addressed. Functional relationships for the mean and variance of the residence times are derived. The effects of users' mobility patterns and the size of quality zones on the functional relationships are also evaluated. Finally, for assumed negative exponential probability density functions of the residence times in the different quality zones (and considering the mean cell residence time to the standard deviation of the cell residence time ratio), the conditions under which the cell residence time can be accurately modeled by the negative exponential distribution are investigated.