The growing interest in wireless systems and networks has led to the first Wireless LAN (WLAN) protocols. The Medium Access Control (MAC) layer protocols of such protocol suites are of key importance. The Radio Equipment and Systems (RES) Technical Committee of the European Telecommunications Standards Institute has proposed the High PErformance Radio LAN (HIPERLAN) protocol suite. In this paper we present, study, analyze and evaluate the performance of the Channel Access Control layer (lower sublayer of the MAC layer) of the HIPERLAN protocol suite for real-time traffic. Numerical results from both analysis and simulation are presented, so that the issues involved are better understood.