WiMAX is intended for fourth generation wireless mobile communications where a group of users are provided with a connection and a fixed length queue. In present literature traffic of such network is analyzed based on the generator matrix of the Markov Arrival Process (MAP). In this paper a simple analytical technique of the two dimensional Markov chain is used to obtain the trajectory of the congestion of the network as a function of a traffic parameter. Finally, a two state phase dependent arrival process is considered to evaluate probability states. The entire analysis is kept independent of modulation and coding schemes.