On the insensitivity of user distribution in multicell networks under general mobility and session patterns

The location of active users is an important factor in the performance analysis of mobile multicell networks, but it is difficult to quantify due to the wide variety of user mobility and session patterns. In particular, the channel holding times in each cell may be arbitrarily distributed and dependent on those in other cells. In this work, we study the stationary distribution of users by modeling the system as a multi-route queueing network with Poisson inputs. We consider arbitrary routing and arbitrary joint probability distributions for the channel holding times in each route. Using a decomposition-composition approach, we show that the user distribution (1) is insensitive to the user movement patterns, (2) is insensitive to general and dependent distributed channel holding times, (3) depends only on the average arrival rate and average channel holding time at each cell, and (4) is completely characterized by an open network with M/M/∞ queues. This result is validated by experiments with the Dartmouth user mobility traces.