Spatial queueing for analysis, design and dimensioning of Picocell networks with mobile users

In this work, we characterize the performance of Picocell networks in the presence of moving users. We model various traffic types between base-stations and mobiles as different types of queues. We derive explicit expressions for expected waiting time, service time and drop/block probabilities for both fixed as well as random velocity of mobiles. We obtain (approximate) closed form expressions for optimal cell size when the velocity variations of the mobiles is small for both non-elastic as well as elastic traffic. We conclude from the study that, if the expected call duration is long enough, the optimal cell size depends mainly on the velocity profile of the mobiles, its mean and variance. It is independent of the traffic type or duration of the calls. Further, for any fixed power of transmission, there exists a maximum velocity beyond which successful communication is not possible. This maximum possible velocity increases with the power of transmission. Also, for any given power, the optimal cell size increases when either the mean or the variance of the mobile velocity increases.