Abstract: Abstract That every node should have the same value of contention window (Cw) was first vertisified in a WLAN by tormulating resource allocation as a utility maximization optimal problem, then the relation between the optimal value of Cwand the number of nodes was obtained by maximizing the total network utility with constrains of minimizing collision probability. A new retransmission algorithm was proposed which uses an optimal shared Cw. Due to the same Cw，the proposed algorithm can effectively overcome the unfairness of BEB algorithm and and improve throughput Simulation results validate our conclusion.

Key words: Utility, Resource allocation, Optimization, I3ackoff algorithm, Fairness, WLANs