Most of works in modeling the spectrum sharing of Cognitive Radio Ad Hoc Networks (CRAHNs) ignored the relationships between processes of using primary channels and that of using secondary channels.Some works considered the relationship and set up simplified queue-based model.However

they are not accurate in analysing the performance of CRAHNs.The main challenge may come from the complexity of setting up states transfer graph and that of computation in the multiple-dimensions Markov model.This paper copes with the challenge by a novel method.We decompose the complex original model into multiple 2-D models which are much easier to analyse

and then compose them all into a structured 3-D Markov model

which is arbitrary order extendable and programmable computation of the stable probability.By the new model

the performance of CRAHNs with an arbitrary number of primary channels and secondary channels can be evaluated .Extensive experimental results testify the validity of the proposed model.