Rapid changes in mobile techniques have always been evolutionary, and the deployment of 4G Long Term Evolution (LTE) networks will be the same. It will be another transition from Third Generation (3G) to Fourth Generation (4G) over a period of several years, as is the case still with the transition from Second Generation (2G) to 3G. As a result, mobile operators must look for strategies and solutions that will enhance their legacy 3G networks, while addressing their 4G deployment requirements without involving a "forklift" upgrade. Mobile subscribers have a certain expectation for their experience of mobile data and voice services that the wireless environment has not fully met yet since the speed at which they can access their mobile services has been limited. On the other hand, mobile operators realize that if they are to succeed in today's mobile communications landscape, they must address the quality of service for their subscribers. Simply adding more bandwidth to accommodate increased traffic is an expensive alternative. How to do more with less? The mobile operators need to minimize Capital Expenditure/Operation Expenditure (CAPEX/OPEX) and maximize subscriber usage. They need to ensure that the mobile network is operating optimally over their capacity planning horizon and make further capital investment in expanding the network infrastructure when the Quality of Service (QoS) falls below their set goal based on the customer expectations. Hence the time to upgrade the core network should coincide with the investment planning horizon. However, since the deployment of 4G LTE networks is a new challenge technically, there are still some unanswered questions on how to dimension the 4G LTE networks for a given scenario and predict the traffic of 4G LTE networks in a long term. The purpose of this research is to study the traffic planning and performance modeling for the evolved packet core networks of LTE network. I created the quantitative algorithms to dimension the traffic for 4G LTE networks. The algorithms emulated the differentiated services (DiffServ) over the 4G LTE networks and applied the DiffServ, via the Weighted Fair Queuing (WFQ) scheduling technique, to the specific traffic flow models (M/G/R-PS and M/D/1-PS) which handle different types of traffic (elastic traffic and streaming traffic) in the 4G LTE network. Furthermore, in order to forecast the chronically increased traffic of 4G LTE networks, I created the algorithms to trend the 4G LTE network traffic via training the historical network performance data This will provide the modeling capability for the mobile operators to plan their capacity increase to match their capital investment horizon and maintain their desired QoS throughout this horizon. Several quantitative algorithms have been applied to train the measured network performance data to find the optimal adjusted threshold of network capacity. After the testing on the reliability, robustness, and external validity, it is concluded that the approach of an improved stochastic gradient boosting shows the best goodness of fitting for calibrating the model for the least prediction error in forecasting the prospective traffic for the next planning horizon. The mobile operators need to minimize their CAPEX/OPEX while planning their network expansion to meet their desired level of service quality. Optimizing investment in the evolution of the 4G network is a limitation of the current research. In particular the CAPEX is determined by the specific network equipment and vendors that the mobile operator uses in planning its networks. I have outlined the steps necessary to conduct the cost analysis in conjunction with the network planning and dimensioning based on specific planning scenario to allow the mobile operators to evaluate their alternative investment options. A case study is provided in the Appendix to approximately estimate the CAPEX/OPEX for a given network scenario. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]