In this work, we develop a novel mathematical model to analyze different location update protocols for mobile cellular network. Our model can capture many important features of user movements, such as geographically dependent movement, directional movement and non-exponential distribution of cell dwell times. We propose to use the transient method to predict the location of a mobile user. This method is efficient and, more importantly, able to address the temporal change in the current location of a mobile user. Therefore, the accuracy of the prediction of the location of a user can be enhanced.We also propose a new location update protocol which can attain a lower tracking cost and also adapt to different mobility patterns. Transient performance analysis is also carried out and the results are compared with other protocols.