New call blocking versus handoff blocking in cellular networks

In cellular networks, blocking occurs when a base station has no free channel to allocate to a mobile user. One distinguishes between two kinds of blocking, the first is called new call blocking and refers to blocking of new calls, the second is called handoff blocking and refers to blocking of ongoing calls due to the mobility of the users. We first provide explicit analytic expressions for the two kinds of blocking probabilities in two asymptotic regimes, i.e., for very slow mobile users and for very fast mobile users, and show the fundamental differences between these blocking probabilities. Next, an approximation is introduced in order to capture the system behavior for moderate mobility. The approximation is based on the idea of isolating a set of cells and having a simplifying assumption regarding the handoff traffic into this set of cells, while keeping the exact behavior of the traffic between cells in the set. It is shown that a group of 3 cells is enough to capture the difference between the blocking probabilities of handoff call attempts and new call attempts.