CONTINUITY OF A QUEUEING INTEGRAL REPRESENTATION IN THE M 1 TOPOLOGY By Guodong Pang and Ward Whitt

0 h(y(s)) ds, t ≥ 0, mapping a function x into a function y, when the underlying function space D is endowed with the Skorohod M1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes, as can occur with bursty arrival processes or service interruptions. The proof of M1continuity is based on a new characterization of the M1 convergence, in which the time portions of the parametric representations are absolutely continuous with respect to Lebesgue measure, and the derivatives are uniformly bounded and converge in L1.