City taxi service systems have been empirically studied by a number of data-driven methods. However, their underlying mechanisms are hard to understand because the present mathematical models neglect to explain a (whole) taxi service process that includes a pair of on-load phase and off-load phase. In this paper, by analyzing a large amount of taxi servicing data from a large city in China, we observe that the taxi service process shows different temporal and spatial features according to the on-load phase and off-load phase. Moreover, our correlation analysis results demonstrate the lack of dependence between the on-load phase and the off-load phase. Hence, we introduce two independent random walk models based on the Langevin equation to describe the underlying mechanism and to understand the temporal and spatial features of the taxi service process. Our study attempts to formulate the mathematical framework for simulating the taxi service process and better understanding of its underlying mechanism.