The many-server, heavy traffic limiting regime for the $GI/M/N$ queue was first proposed by Shlomo Halfin and Ward Whitt in 1981. Since that time, the extension of their results to the more general $GI/GI/N$ queue has remained an important open problem. In this talk, we will provide a solution to a substantial portion of this problem by extending Halfin and Whitt's results to the class of service time distributions which possess a continuous density. These results are relevant to the design and control of modern, large-scale telephone call centers, where Halfin and Whitt's regime is used as a popular modeling tool and the service times are typically not exponentially distributed.
