The Many Server Queue in Heavy Traffic
Anatolii Puhalskii, Associate Professor of Mathematics, University of Colorado, Boulder
Monday, September 14, 2009
4:00 p.m., 223 Weber
This talk is concerned with a generalization of the asymptotics discovered by Halfin and Whitt (a.k.a. the Halfin-Whitt regime). A many server queue with both the number of servers and the arrival rate going to infinity are considered. No critical loading condition is assumed. A limit theorem on convergence in distribution for the queue length process is established. The trajectories of the limit process may have discontinuities of the second kind. Under additional hypotheses, the limit has rightcontinuous with lefthand limits trajectories and the convergence in distribution holds for the Skorohod J_1-topology. A number of extensions of the main result as well as open questions are outlined.