Approximation of blocking probabilities in mobile cellular networks with channel borrowing

Channel borrowing has been widely adopted in mobile cellular networks as a compromise between fixed channel assignment and dynamic channel assignment. Various channel borrowing schemes have been proposed in the literature with their performance, typically in terms of blocking probability, obtained by computer simulations. However, analytical approximation methods are much more computationally effective and practically useful for performance analysis of mobile cellular networks. In this paper, we model mobile cellular networks with channel borrowing as overflow loss systems. We present two methods for approximation of blocking probabilities in such systems, one based on the classical Erlang fixed point approximation (EFPA) approach, and the other derived from the recently established information exchange surrogate approximation (IESA) framework. Comprehensive results of both EFPA and IESA are provided and compared against simulation results. We demonstrate for a wide range of scenarios that IESA is more accurate in evaluating blocking probabilities than EFPA. To the best of our knowledge, our proposed approximation framework is the first workable approach in terms of accuracy and computational efficiency for cellular networks with consideration to mobility of calls and a channel borrowing mechanism.