Abstract
We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion.
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Bekker, R. Queues with Lévy input and hysteretic control. Queueing Syst 63, 281 (2009). https://doi.org/10.1007/s11134-009-9123-z
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DOI: https://doi.org/10.1007/s11134-009-9123-z
Keywords
- M/G/1 queue
- Storage process
- Lévy process
- Lévy exponent
- Double reflection
- Workload distribution
- Two-state strategy
- Hysteretic control