Controlled sharing of the wireless link by different packet streams is critical in transporting multimedia traffic across wireless networks. Consequently, it has been treated as providing support for quality of service (QoS) in medium access control (MAC) protocols. This paper proposes a distributed class-based access scheme whose allocation policy adopts token passing packet scheduling, designed to handle efficiently different service classes of traffic in heavy load wireless networks. The traffic is divided into three classes by QoS specifications and packet characteristics, and served with asymmetric exhaustive discipline. The probability generating function based on imbedded Markov chain for this discrete-time system is derived. We employ basic queuing analysis methodologies, calculate the average buffer size of each class queue at polling instants and then apply Little's law to find the average delay. Experiments are conducted to validate the new strategy, and the performance is analyzed and evaluated. Finally, we visualize and compare how the relative variable parameters effect on system characteristics.