Analysis of location area residence time in mobile cellular networks

In order to accurately analyze the performance of location registration schemes, a proper mobility model of user equipment (UE) is essential. In previous work by Wang et al. [10], it is asserted that if the cell residence time of UE follows an exponential distribution and a fluidflow model is adopted, then location area (LA) residence time of UE also follows an exponential distribution. However, this result is incorrect, because the LA residence time of UE, which is composed of various combinations of cell residence times, cannot follow an exponential distribution in general. In this study, to prove that Wang et al.'s result is incorrect, we first obtain accurate analytical results for LA residence time for a small LA that is composed of 7 hexagonal cells, and then show that analyzed LA residence time does not follow an exponential distribution. Furthermore, we perform computer simulations for various situations, and then show that, through a goodness-of-fit test, simulated LA residence time cannot follow an exponential distribution.