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 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. Through a decomposition-composition approach, we derive a closed-form expression for the joint stationary distribution for the number of users in all cells. The stationary user distribution (1) is insensitive to the user movement patterns, (2) is insensitive to general and dependently 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. We use the Dartmouth trace to validate our analysis, which shows that the analytical model is accurate when new session arrivals are Poisson and remains useful when non-Poisson session arrivals are also included in the data set. Our results suggest that accurate calculation of the user distribution, and other associated metrics such as the system workload, can be achieved with much lower complexity than previously expected.