Wireless Networks

, Volume 24, Issue 4, pp 1327–1342 | Cite as

Performance model for two-tier mobile wireless networks with macrocells and small cells

  • Vicente Casares-Giner
  • Jorge Martinez-Bauset
  • Xiaohu Ge


A new analytical model is proposed to evaluate the performance of two-tier cellular networks composed of macrocells (MCs) and small cells (SCs), where terminals roam across the service area. Calls being serviced by MCs may retain their channel when entering a SC service area, if no free SC channels are available. Also, newly offered SC calls can overflow to the MC. However, in both situations channels may be repacked to vacate MC channels. The cardinality of the state space of the continuous-time Markov chain (CTMC) that models the system dynamics makes the exact system analysis unfeasible. We propose an approximation based on constructing an equivalent CTMC for which a product-form solution exist that can be obtained with very low computational complexity. We determine performance parameters such as the call blocking probabilities for the MC and SCs, the probability of forced termination, and the carried traffic. We validate the analytical model by simulation. Numerical results show that the proposed analytical model achieves very good precision in scenarios with diverse mobility rates and MCs and SCs loads, as well as when MCs overlay a large number of SCs.


Two-tier mobile wireless networks Overflow and repacking Performance evaluation Blocking probability Forced termination probability 



Authors would like to thank you the anonymous reviewers for the review comments provided to our work that have decisively contributed to improve the paper. Most of the contribution of V. Casares-Giner was done while visiting the Huazhong University of Science and Technolgy (HUST), Whuhan, China. This visit was supported by the European Commission, 7FP, S2EuNet project. The authors from the Universitat Politècnica de València are partially supported by the Ministry of Economy and Competitiveness of Spain under grant TIN2013-47272-C2-1-R and TEC2015-71932-REDT. The research of Xiaohu Ge was supported by the National Natural Science Foundation of China (NSFC) grant 61210002, the Fundamental Research Funds for the Central Universities grant 2015XJGH011, and China International Joint Research Center of Green Communications and Networking grant 2015B01008.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Universitat Politècnica de ValènciaValenciaSpain
  2. 2.Huazhong University of Science and TechnologyWuhanPeople’s Republic of China

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