A novel backoff algorithm is proposed in carrier sense multiple access with collision avoidance (CSMA/CA) based medium access control (MAC) protocols for clustered sensor networks. Firstly, every node should have the same value of contention window (CW) in a cluster, when formulating resource allocation is considered as a model with maximum utility optimization. Then, it is assumed that all nodes have the same CW and gain the relation between the optimal value of CW and the number of nodes by maximizing the total network utility with constrains of minimizing collision probability. The result i...