Variability of location management costs with different mobilities and timer periods to update locations

In this article, we examine the Location Management costs in mobile communication networks utilizing the timer-based method. From the study of the probabilities that a mobile terminal changes a number of Location Areas between two calls, we identify a threshold value of 0.7 for the Call-to-Mobility Ratio (CMR) below which the application of the timer-based method is most appropriate. We characterize the valley appearing in the evolution of the costs with the timeout period, showing that the time interval required to reach 90% of the stabilized costs grows with the mobility index, the paging cost per Location Area and the movement dimension, in opposition to the behavior presented by the time interval that achieves the minimum of the costs. The results obtained for CMRs below the suggested 0.7 threshold show that the valley appearing in the costs tends to disappear for CMRs within [0.001, 0.7] in onedimensional movements and within [0.2, 0.7] in two-dimensional ones, and when the normalized paging cost per Location Area is below 0.3.