One building block to provide service quality is queueing disciplines such as Random Early Detection (RED). Besides the topic of service differentiation (e.g., Differentiated Services), data flows within a service class are expected to receive the same service quality which is expressed in the service quality metric ‘fairness’. This document evaluates traffic phase effects when using RED gateways in conjunction with UDP-based constant bit rate sources. These effects can lead to an unfair division of the available bandwidth among CBRdata flows with the same bandwidth share. It is shown that the introduction of randomization may help to improve the fairness.