Local area networks often comprise nodes that run applications that belong to different traffic classes, with each class having different bandwidth requirements. Traditional Medium Access Control (MAC) protocols treat all nodes in the same manner. This may lead to a disproportionate allocation of bandwidth to the nodes and, consequently, to significant performance degradation. In this paper, a new MAC algorithm, is presented, that allocates different amounts of bandwidth to the nodes according to their traffic class. The bandwidth allocated to the nodes of each traffic class is proportional to the bandwidth requirements of the nodes of that class. The performance of the proposed Node Classification-based Bandwidth Allocation (NCBA) algorithm is studied via extensive simulation results, which indicate that it achieves a significant performance improvement compared to the well-known TDMA scheme. Overall, the new protocol achieves higher throughput, lower delay and exhibits a higher delay Fairness compared to TDMA for various network configurations, under asymmetric bursty traffic.