Design of location erea(LA) in a cellular network is to partition the network into clusters of cells so as to minimize the cost of location updating and paging. Most research works dealing with the LA design problem assume that the call. arrival rate and mobile flow rate are fixed parameters which can be estimated independently. In this aspect, most Problems addressed so far are deterministic LA design problems(DLADP), known to be NP hard. The mobile flow and call arrival rate are, however, varying with time and should be treated simultaneously because the call arrival rate in a cell during a day is influenced by the change of a population size of the cell. This Paper Presents a new model on IA design problems considering the time-dependent call arrival and mobile flow rate. The new model becomes a stochastic LA design problem(SLADP) because It takes into account the possibility of paging waiting and blocking caused by the changing call arrival rate and finite paging capacity. Un order to obtain the optimal solution of the LA design problem, the SIADP is transformed Into the DLADP by introducing the utilization factor of paging channels and the problem is solved iteratively until the required paging quality is satisfied. Finally, an illustrative example reflecting the metropolitan area, Seoul, is provided and the optimal partitions of a cell structure are presented.