In this paper random access problem for the OFDMA based communication system is addressed in perspec-tive of service differentiated non cooperative game for gaining distributed control over the system. In order to provide diverse QoS demands from users, an access priority based scheme for effectively supporting various ASCs (Access Service Classes) according to the different QoS (Quality of Service) require-ment profiles is proposed and analyzed by using game theory. Performance analysis of the proposed random access protocol, SDNcRA is made in terms of success probability attained and delay encountered versus number of mobile terminals present in the system. Two ASCs, ASC0 and ASC1, are treated in this paper and it is varified that ASC0 UEs which have higher priority than ASC1 UEs always receive high success probability and less delay.