In this paper, we present an exact analysis and an efficient matrix-analytic procedure to numerically evaluate the performance of cellular mobile networks with hand-off. In high-capacity micro-cell cellular radio communication networks, a cell boundary crossed by moving users can generate many hand-off attempts. This paper considers such a priority scheme that some channels and buffers are reserved for hand-off calls to reduce the forced termination of calls in progress. Performance characteristics we obtained include blocking probability, channel utilization, average queue length and average waiting time for hand-off calls. Using the matrix-analytic solution for the stationary state probability distribution, we also derive the probability distribution of the waiting time of a hand-off call. Numerical results show how priority can be provided to hand-off calls according to the number of reserved channels and buffer size. They also clarify the effect of the hand-off priority scheme on the standard deviation of waiting time of a hand-off call.