Diffusion approximation of the stationary distribution of a two-level single server queue
| Autor: | Miyazawa, Masakiyo |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider a single server queue which has a threshold to change its arrival process and service rate by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a single server queue whose arrival process and service rate may be changed. To get its performance in tractable form, we study the limit of the stationary distribution of the queue length in this two-level queue under scaling in heavy traffic. This limit corresponds to its diffusion approximation. It is shown that this limiting distribution is truncated exponential (or uniform if the drift is null) below the threshold level and exponential above it under suitably chosen system parameters. This result is proved using the so called BAR approach studied in Braverman, Dai and Miyazawa (2017, 2023) and Miyazawa (2017, 2023). We also intuitively discuss about a diffusion process corresponding to the limit of the stationary distributions. Comment: 36 pages, 2 figure, to appear in Advances in Applied Probability 57.2 (June 2025) |
| Databáze: | arXiv |
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