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An analytic model of cellular mobile communications networks with instantaneous movement is investigated in this paper. This cellular mobile network is showed to be equivalent to a queueing network and furthermore the equilibrium distribution of this cellular mobile network is proved to have a product form. The explicit expressions for handoff rates of calls from one cell to another, the blocking probability of new calls and handoff calls are then obtained. Actual call connection time (ACCT) of a call in this cellular mobile network is characterized in detail, which is the total time a mobile user engages in communications over the network during a call connection and can be used to design appropriate charging schemes. The average ACCT for both complete call and incomplete call, as well as the probability for a call to be incomplete or complete, are derived. Our numerical results show how the above measures depend on the new call arrival process for some specific reserved channels numbers in each cell. The results presented in this paper are expected to be useful for the cost analysis for updating location and paging in cellular mobile network.