In this article, we propose a new mobility model, for a mobile and geographic cross-layer architecture. This cross-layer architecture allows service differentiation between real-time and best-effort traffic, for a mobile internet of things ( IoT ) network. We present a mathematical model, which works on the parameters of the MAC layer and the network layer. The mathematical model makes it possible to calculate the throughput between a source object and a destination object (gateway), under conditions of stable queues. We use the positional (geographic) information in the mathematical model of the proposed cross-layer architecture, to study the impact of mobility on the performance of the proposed mathematical model. The proposed mobility model defines two time intervals, the first interval for communication (transmission and reception of data without mobility at the same time), and the second time interval for the mobility of objects of the IoT network (without communication at the same time). The results show that the calculated throughput depends on the position of the objects, as well as the probability of transmission. Finally, we study the effect of distance and speed on the performance of the proposed cross-layer architecture.