**4.2 Channel rearrangement effect**

In hierarchical overlaying cellular networks, traffic overflow between the overlaying tiers is used to increase the utilization of the available capacity. The arrival process of overflow traffic has been verified to be correlated and bursty. This characteristic has brought great challenges to performance evaluation of hierarchical networks. In most published works, the discussion is focussed on traffic loss analysis in homogenous hierarchical networks, e.g. micro/macro cellular phone systems as in the numerical analysis below. In the paper (Huang et al., 2008), the authors address the problems of performance evaluation in more complicated scenarios by taking account of heterogeneity and user mobility in hierarchical networks. They present an approximate analytical loss model. The loss performance obtained by our approximated analytical model is validated by simulation in a heterogeneous multi-tier overlaying system.

Fig. 12 shows the dependence of revenue on channel rearrangement from macro-cell to micro-cell. We are looking for maximum revenue when low-mobility calls cost one unit and high-mobility calls cost *K* = 3 units.
