Formal Approximations of the Transient Distributions of the M/G/1 Workload Process
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917973791342592 |
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| author | Michel, Fabian Siegle, Markus |
| author_facet | Michel, Fabian Siegle, Markus |
| contents | This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approximate specific queues on R with one-sided Lévy input, such as the M/G/1 workload process, with a finite-state Markov chain. The transient distribution of the original process is approximated by a distribution with a density which is piecewise constant on the state space. Easy-to-calculate error bounds for the difference between the approximated and actual transient distributions are provided in the Wasserstein distance. Our method is fast: to achieve a practically useful error bound, it usually requires only a few seconds or at most minutes of computation time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal Approximations of the Transient Distributions of the M/G/1 Workload Process Michel, Fabian Siegle, Markus Probability 60G51 (Primary) 60K25, 60J22 (Secondary) G.3 This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approximate specific queues on R with one-sided Lévy input, such as the M/G/1 workload process, with a finite-state Markov chain. The transient distribution of the original process is approximated by a distribution with a density which is piecewise constant on the state space. Easy-to-calculate error bounds for the difference between the approximated and actual transient distributions are provided in the Wasserstein distance. Our method is fast: to achieve a practically useful error bound, it usually requires only a few seconds or at most minutes of computation time. |
| title | Formal Approximations of the Transient Distributions of the M/G/1 Workload Process |
| topic | Probability 60G51 (Primary) 60K25, 60J22 (Secondary) G.3 |
| url | https://arxiv.org/abs/2504.01193 |