Broadband packet switches handling an asynchronous-time-division-multiplexing type protocol format, e.g. Starlite, can achieve buffer efficiencies by sharing buffers between output ports. It is shown that the number of buffers required with sharing, for random traffic, would be overestimated by as much as 30% at 90% traffic load if the negative correlations that naturally exist, for this type of traffic, between packet streams destined for different output ports were not taken into account. In general, the discrepancy increases as the traffic load increases, and decreases as the switch size increases. A general approach is developed for the analysis of set of queues to which the arrival streams are correlated, which could be used to assess the impacts on shared buffer requirements due to other types of stream correlation (e.g. positive correlations) that may result from other traffic assumptions.>