Heavy-traffic limits for many-server queues with service interruptions

We establish many–server heavy–traffic limits for G/M/n+M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue–length process, where the limit is an ordinary differential equation in a two–state random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queue–length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jump–diffusion process in the QED regime and an O–U process driven by a Levy process in the ED regime (and for infinite–server queues). A stochastic–decomposition property of the steady–state distribution of the limit process in the ED regime (and for infinite–server queues) is obtained.