On the impact of mobility in cellular networks

It is well-known that mobility increases the throughput of wireless networks, and the main objective of this paper is to show that, depending on the system's parameters, delay can actually be negatively impacted. To do so, we study a Markovian model where users arrive to the network according to a Poisson process with rate $\lambda$ and then move at speed $\alpha \ \epsilon [0, \infty)$ between nodes while in service. Given the complexity of the model, we resort to approximation techniques in order to get insight into the influence of the speed $\alpha$ on the mean delay. Our main findings are the following: •in the case where the network consists of two nodes, delay is monotone in $\alpha$ for small values of $\lambda$ . We furthermore explicit a constant $C$ such that delay is increasing if and only if $C < 0$ ; •in the general case, we provide numerical results showing that delay is not necessarily monotone in $\alpha$ . However, we compare the two extreme cases with 0 and infinite speed, and find that for small values of $\lambda$ , delay is worse with infinite speed than with 0 speed if and only if $C < 0$ . Finally, an intuitive interpretation of this constant $C$ is provided.