This paper analyses bandwidth allocation schemes for managing real-time applications (Variable Bit Rate video and voice) in a CRMA network. A methodology to compute the Quality of Service (QoS) experienced by variable bit rate (VBR) video and voice sources is proposed. As VBR video applications only tolerate extremely low packet loss rates (< 10-8), we need a computational approach to estimate very low tail probabilities. Studying the QoS with a simulation technique is not feasible, because computational costs make it almost impossible to estimate tail distribution probabilities lower than 0.01-0.001. Therefore, to achieve this target, we propose a model which represents a CRMA network's worst case behaviour (i.e. a scenario with maximum network congestion), and which can be solved analytically. By solving this model for different bandwidth allocation schemes, we can obtain the corresponding bounds on the QoS experienced by VBR video users. Finally, for those bandwidth allocation schemes which provide an acceptable QoS for VBR video traffic, we also estimate (via a trace-driven simulation) the QoS achieved by voice users.