Heavy-traffic Limits For Waiting Times In Queues System With Ababdonment

The main contents of the paper are to establish heavy-traffic stochastic-process limits for wating times in mang-server queues with customer abandonment and waiting space. i.e,G/G/n/mn+G moder have a general arrival and service process, n servers, mn waiting space,and first-come-first-served service discipline(FCFS). We establish heavy-traffic stochastic-process limits for wating times that M/M/n/mn+M moder in the quality-and-efficency-driven (QED) regime and the efficency-driven (ED) regime. We treat customer abandonment by studing the limiting behavior of the queueing models with arrivals turned off at some time t. To prove stochastic-process limits for virtual waiting times, we apply a two-parameter version of Puhalskii's invariance principle for first passage times.