Radio is a valuable resource for wireless/mobile communication systems. In this paper, we present an ef-ficient algorithm using a novel triangle communication model to synchronize processes effectively by searching for free channels for wireless mobile communication systems. A geographical area controlled by a Mobile Switching Center (MSC) is divided into many small hexagonal regions called cells. Each cell in a sub-cluster can effectively collect channel information from the first tier of co-channel cells through the triangle communication model. The performance of the communication model is characterized in terms of message complexity, response time and failure locality. For fair evaluation, we introduce a novel metric, which is called Accumulated Failure Locality (AFL). The triangle communication model improves message complexity,response time and AFL of the algorithm. With AFL, we examine our algorithm, and produce an AFL vectr. We discuss the algorithm and prove its correctness. We also show that the algorithm requires at most O(Nsc) messages,where Nsc is the number of cells in a sub-cluster.This is compared to the algorithms [3] which requires O((Ng)2), where Ng is the number of channel groups in the large bandwidth allocated to the system.