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

Pang, Guodong; Whitt, Ward

We establish many-server heavy-traffic limits for G/M/n + M queueing models, allowing cus- tomer 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 asymptoti- cally 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-decompostion property of the steady-state distribution of the limit process in the ED regime (and for infinite-server queues) is obtained.

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Also Published In

Title
Queueing Systems
DOI
https://doi.org/10.1007/s11134-009-9104-2

More About This Work

Academic Units
Industrial Engineering and Operations Research
Published Here
September 19, 2017