We propose and analyze a traffic model of a cellular radio communication network with an arbitrary cell connection and arbitrary probabilistic movement of mobiles between the cells. Our analytic model consists of birth-and-death processes for individual cells connected by the numerical adjustment of hand-off rates. This approximation is validated by simulation. We evaluate the probabilities of the immediate loss, the completion, and the forced termination during hand-off for an arbitrary call in the network. Our numerical examples reveal the cases in which the increase in the generation rate of new calls results in the increase in the loss probability without affecting much the probability of forced termination in a limited service area.