We examine the delay performance of packets from constant-bit-rate (CBR) traffic whose delay is affected by non-real-time traffic. The delay performance is analyzed by solving the nD/D/1 queue with vacations. We obtain an exact and closed form solution, hence obviating the need of any approximations or numerical Laplace inversions. We then provide various numerical results for low-bit-rate transmission links, in which packets can experience large delay. From our quantitative evaluation, we conclude that there exists an optimum packet size for a given delay bound. In extremely slow links, such as modem links, transmission control protocol (TCP) packets should be segmented to reduce the CBR delay. We therefore investigate the delay impact of ...