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Dynamic resource availability and lack of central control unit offer many challenges while designing medium access control (MAC) protocol for a distributed cognitive radio network (DCRN). In this paper, we propose a novel MAC design for DCRN which provides an efficient approach to address quality of service (QoS) requirements of delay sensitive applications by defining higher priority to such applications during channel reservation. It also combats other major challenges such as efficient spectrum utilization, multi-channel hidden terminal problem (MHTP) and collision with primary user (PU) due to sensing error at SU. We develop an analytical framework to study the performance of the proposed protocol. We then compare the performance of proposed protocol with those of two existing protocols. Comparison results show that proposed MAC outperforms the existing protocols by providing better throughput and reducing DCRN users' collision probability with PUs in presence of sensing error. The results achieved from the analytical model and validated by simulations show that our simple yet efficient design identifies and fulfils the QoS requirements of delay sensitive applications, achieves excellent spectrum utilization, shows superb robustness in presence of sensing errors and handles MHTP effectively.