The Spatial Effect of Mobility on the Mean Number of Handoffs: A New Theoretical Result

The mean number of handoffs is a fundamental performance measure in any mobile system, as it directly relates to the signaling load in the network as well as to the delivered QoS. As the mobile services are evolving from simple cellular voice calls towards media and data sessions, and as cellular providers are reinventing their businesses by incorporating third party services, the handoff rate will even play a more pivotal role. This is because future sessions are expected to last longer than voice calls and users are more likely to roam into other networks. Existing results provide an estimate of the mean number of handoffs in networks composed of an infinite number of access gateways and hence consider neither the topological arrangement of the gateways nor the mobility patterns between them. In this paper, we obtain a closed form solution for the mean number of handoffs under generic assumptions of two- dimensional Markovian mobility patterns, spatial arrangement of the access gateways, as well as generic session times and gateway residence times. Our solution unveils a new insight into mobility foundations as it shows that the consideration of the mobility pattern and the access gateways' layout simply transforms the known equation for the mean number of handoffs of an infinite network size from scalar to vector representation. We demonstrate that the mean number of handoffs is a non-linear function of the gateway spatial arrangement and user mobility.