For the Radio Channel Allocation (RCA) of wireless net works, how to efficiently allocate the limited number of channels to achieve high throughput is a challenging problem. The major difficulty in solvin g the RCA problem is to maximize the throughput of the entire network using the min-max optimization scheme. Usually, it is solved by using various heur istic methods, which are known to be NP-hard and have unknown computational scales. In this paper, w e analyze a typical RCA algorithm for IEEE 802.11 based wireless networks including wireless LANs (WL ANs) and wireless mesh networks, namely, the distributed heuristic algorithm (DHA) [2], by using both analytical and statistical analysis in terms of the computational scale (CS) of the method. The CS of an algorithm is defined as the number of channel reallocation times until the network reaches a conv ergence state. By extensive simulations, we demonstrate that DHA reaches the convergence state in finite steps. The total number of channel reallocations is a log-logistic distribution. Based on all the possible network configurations, we develop a method to estimate the CS. We find that the overall upper limit of the CS for a network is O( I), where I is the number of access points (APs) or mesh router s that are responsible for allocating the available radio channels.