Analytical models for call blocking and dropping in sectorized cellular networks with fractional frequency reuse

In this paper, we construct mathematical models to analyze the probabilities of new call blocking and handoff call (HC) dropping for a sectorized cellular network with fractional frequency reuse (FFR). Because a sectorized FFR network (SFN) consists of two areas, the super group (SG) and the regular group (or sectors), three different types of HCs may happen when a mobile station (MS) moves from the SG to a sector, from a sector to the SG, or from one sector to another sector. To characterize three types of HCs, we first derive the area transition probability, which is defined as the reciprocal of MS's average residence time in an area (i.e., sector or SG). Moreover, we construct the model of Markov chains and derive the state transition rates. Then on the basis of the stationary probabilities of Markovian states, we derive the three types of blocking probabilities of new calls and two types of dropping probabilities of HCs. Finally, we conduct extensive numerical simulations. From the results of numerical simulations, we reveal two important rules for choosing the optimal radius of the SG, with which the system blocking and dropping probability can be effectively minimized. Copyright © 2014 John Wiley & Sons, Ltd. We construct Markov chain‐based models to aim at minimizing the system blocking and dropping probability in a sectorized cellular network with fractional frequency reuse (or SFN for short). Two discovered rules for choosing the optimal radius of the super group (SG) are as follows: (i) for an SFN with a large number of sectors, a large radius of the SG is preferred, and (ii) for an SFN with higher moving speeds of mobile stations, a small radius of the SG is preferred.