In this paper, a new technique for cross layer design, based on present Eb/N0 (bit energy per noise density) ratio of the connections and target values of the Quality of Service (QoS) information parameters from MAC layer, is proposed to dynamically select the Modulation and Coding Scheme (MCS) at the PHY layer for WiMAX Broadband Wireless Access (BWA) networks. The QoS information parameter includes New Connection Blocking Probability (NCBP), Hand off Connection Dropping Probability (HCDP) and Connection Outage Probability (COP). In addition, a Signal to Interference plus Noise Ratio (SINR) based Call Admission Control (CAC) algorithm and Queue based Scheduling algorithm are integrated for the cross layer design. An analytical model using the Continuous Time Markov Chain (CTMC) is developed for performance evaluation of the algorithms under various MCS. The effect of Eb/No is observed for QoS information parameters in order to determine its optimum range. Simulation results show that the integrated CAC and packet Scheduling model maximizes the bandwidth utilization and fair allocation of the system resources for all types of MCS and guarantees the QoS to the connections.