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

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.