Approximating fluid queues with quasi birth-and-death processes with rational arrival process components
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910917803900928 |
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| author | Bean, Nigel Lewis, Angus |
| author_facet | Bean, Nigel Lewis, Angus |
| contents | A fluid queue is a stochastic process which moves linearly with a rate that is determined by the state of a continuous-time Markov chain (CTMC). In this paper we construct an approximation to a fluid queue using a quasi birth-and-death process with rational arrival process components (QBD-RAP) and prove weak convergence via convergence of generators. The primary motivation for constructing the new approximation is to achieve a better approximation accuracy than existing methods while also ensuring that all approximations to probabilities have all probabilistic properties, such as non-negativity and bounded above by 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating fluid queues with quasi birth-and-death processes with rational arrival process components Bean, Nigel Lewis, Angus Probability A fluid queue is a stochastic process which moves linearly with a rate that is determined by the state of a continuous-time Markov chain (CTMC). In this paper we construct an approximation to a fluid queue using a quasi birth-and-death process with rational arrival process components (QBD-RAP) and prove weak convergence via convergence of generators. The primary motivation for constructing the new approximation is to achieve a better approximation accuracy than existing methods while also ensuring that all approximations to probabilities have all probabilistic properties, such as non-negativity and bounded above by 1. |
| title | Approximating fluid queues with quasi birth-and-death processes with rational arrival process components |
| topic | Probability |
| url | https://arxiv.org/abs/2504.17176 |