Cloud Radio Access Networks (CRAN) and Multi-Access Edge Computing (MEC) are two of the many emerging technologies that are proposed for 5G mobile networks. CRAN provides scalability, flexibility, and better resource utilization to support the dramatic increase of Internet of Things (IoT) and mobile devices. MEC aims to provide low latency, high bandwidth and realtime access to radio networks. Cloud architecture is built on top of traditional Radio Access Networks (RAN) to bring the idea of CRAN and in MEC, cloud computing services are brought near users to improve the user's experiences. A cache is added in both CRAN and MEC architectures to speed up the mobile network services. This research focuses on cache management of CRAN and MEC because there is a necessity to manage and utilize this limited cache resource efficiently. First, a new cache management algorithm, H-EXD-AHP (Hierarchical Exponential Decay and Analytical Hierarchy Process), is proposed to improve the existing EXD-AHP algorithm. Next, this paper designs three dynamic cache management algorithms and they are implemented on the proposed algorithm: H-EXD-AHP and an existing algorithm: H-PBPS (Hierarchical Probability Based Popularity Scoring). In these proposed designs, cache sizes of the different Service Level Agreement (SLA) users are adjusted dynamically to meet the guaranteed cache hit rate set for their corresponding SLA users. The minimum guarantee of cache hit rate is for our setting. Net neutrality, prioritized treatment will be in common practice. Finally, performance evaluation results show that these designs achieve the guaranteed cache hit rate for differentiated users according to their SLA. ACKNOWLEDGMENTS I would like to express my deepest gratitude to my project advisor, Dr. Melody Moh, for her excellent guidance, and encouragement throughout the course of this project. My sincere thanks to my committee members, Dr. Robert Chun, and Dr. Teng Moh for their useful comments, and their valuable time for reviewing my work. Special thanks to my husband, for his endless support, and understanding, and for never giving up on me. Special love to my son for his patience, and being flexible to my schedule, and his love for me helped me to keep going. I would like to say my heartily thank you to my mom for her motivation and blessings. Last but not the least, a big thank you for my wonderful family and friends for their moral support. vi