Abstract
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.
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Pang, G., Whitt, W. Heavy-traffic limits for many-server queues with service interruptions. Queueing Syst 61, 167–202 (2009). https://doi.org/10.1007/s11134-009-9104-2
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DOI: https://doi.org/10.1007/s11134-009-9104-2
Keywords
- Many-server queues
- Service interruptions
- Heavy-traffic limits
- Skorohod M 1 topology
- Continuous mapping theorem
- Jump-diffusion process
- Levy-driven O–U process
- Stochastic-decomposition property