what is the best mathematical model which can model the tranmission rate of a routing path of a mobile wireless communication network taking into account the SINR , interference and energy consumption at the nodes?
The most common model is that based on the Sahnon maximum channel transmission capacity C.
where:
C=B log2 (1+S/ (N+I)),
B is the bandwidth of the link, S is the signal where the noise N and the interference I is measured.
The other model of the transmission capacity of a link is that as that determined by the modulation technique and the minimum signal to noise ratio for a given bit error rate.
I suggest you consider the models where the node form a Poisson point process. These are the most tractable and lead to insightful results. For example, check out this work:
K. Stamatiou and M. Haenggi, "Delay Characterization of Multihop Transmission in a Poisson Field of Interference," IEEE/ACM Transactions on Networking, vol. 22, pp. 1794-1807, Dec. 2014.