# The a network. Therefore instead of to

The movements of users in each cell are limited with the road. Therefore the total number of mobile users’ location area boundary crossing is equal to the total number of location update generated in a network. Therefore instead of to calculate the location update generated in a network, the traffic flow in different roads along the boundary of location areas can be calculated. For this reason, the aim of this model is to get a configuration of location areas with the least boundary crossing. Number of roads is R, and roads are are separated into three different groups such as alley, main road and street. The notations used in the following mathematical process are the following: N: is the total number of cells in a network, {1,2,…,N}: The corresponding index set of the cells, K: is the total number of road types, {R_(k_1 ),R_(k_2 ),…,R_(k_(S_k ) ) } : the road set of type k (k=1,2,…,K) S_k: the total number of roads of type , {k_(S_1 ),k_(S_2 ),…,k_(S_(N_(k_S ) ) ) } : the index of cells in order passed by a road of type , N_k,(N_k?N): the total number of the cells passed by a road of type k(k=1,2,…,K,s=1,2,…,S_k )Then, the code used to calculate total number of location areas boundary crossing in busy hour is:NR=?_(k=1)^K??_(s=1)^(S_k)??_(n=1)^(N_(k_s ))?d_(k_(s_n ) k_(s_(n+1) ) )  ?_(k_(s_n ) k_(s_(n+1) ) ), k_(s_n )and k_(s_(n+1) )represent the indexes of two different cells. If cell i and cell j are given to the same location area, d_ij=1 ; or, d_ij=0. ?_(k_(s_n ) k_(s_(n+1) ) ) represents the traffic flow between ck_(s_n ) and cell k_(s_(n+1) ) in a k type road.NR is the total number of location area boundary crossing in a busy hour for all of the network. Because of the hypothesis which have made in the earlier part, if the NR get smaller, it can reduce the cost of location update  As stated above, the total number of the user location areas boundary crossing in a busy hour as the objective of the model in this algorithm is used. The goal of this model is to find a configuration of location area to make as small as possible without violating the constraints.The cell information-based algorithm for location area planning problem has proved its ability to significantly reduce signaling costs by computer simulation. Usage of the coding method based on four-color theorem helps to increase the efficiency of the proposed algorithm. The constraints are fixed when the work is updating and different strategies used in this process. The comparisons of the experimental results show the practical applicability of the algorithm. ?