Joint distribution of numbers of location updates and cell boundary crossings in movement-based location management schemes

The movement-based location management (LM) scheme is a well-known dynamic LM scheme that is relatively easy to implement. In this letter, we derive the joint probability distribution of the number of cell boundary crossings and number of location updates of a mobile terminal, assuming Poisson call arrivals and generally distributed cell residence time, under movement-based LM. The derived movement statistics are used to bound the movement threshold so that the number of location updates is kept within a reasonable range. Numerical results are presented.