The coefficient of variation of queue size for heavy traffic

Consideration is given to the limiting form of the coefficient of variation of queue size, cv, for the case where the arrival rate is only slightly smaller than the service rate. Contrary to the first impression gained from early work on this heavy traffic situation, it is found that cv does not always tend to one. Further investigation reveals that in those cases where cv does tend to one, under certain conditions the limit is approached from above, whereas in other cases cv tends to one from below. An indication of the usefulness of this result in the provision of adequate queueing space for customers is included.