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In this paper, we present Black-Burst-based Quality-of-Service Routing (BBQR), a novel QoS routing protocol for wireless ad-hoc networks. BBQR solves two core problems of QoS routing. First, there is the problem that concurrent route discoveries may fail due to mutual blocking of resources. BBQR avoids this problem by serializing route discoveries, using a distributed, yet highly efficient arbitration scheme. Secondly, there is the problem that routing packets may be lost due to frame collisions on the wireless medium, which may lead to failure of route discoveries, too. BBQR avoids this problem through synchronized route discovery phases and the use of collision-resistant frame encodings with black bursts. Further properties of BBQR are that route discoveries have constant duration and low and bounded communication complexity.