AbstractThis paper considers the range of values of the coefficient of variation of waiting time in some general single-server queueing systems. It is shown that inM/G/1 systems with givenρ, the square of this coefficient increases linearly withm1m3/m22, wheremiis theith moment of the service distribution. This implies always a lower bound, and for some widely used distributions an upper bound as well. A few ranges are illustrated and compared to those implied in twoGI/M/1 systems. The usefulness of knowing such ranges for modelling purposes is explained.