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http://hdl.handle.net/10397/90454
| Title: | Diffusion approximation for fair resource control - interchange of limits under a moment condition | Authors: | Ye, H-Q Yao, DD |
Issue Date: | Aug-2021 | Source: | Mathematics of operations research, Aug. 2021, v. 46, no. 3, p. 869-894 | Abstract: | In a prior study [Ye HQ, Yao DD (2016) Diffusion limit of fair resource control–Stationary and interchange of limits. Math. Oper. Res. 41(4):1161–1207.] focusing on a class of stochastic processing network with fair resource control, we justified the diffusion approximation (in the context of the interchange of limits) provided that the pth moment of the workloads are bounded. To this end, we introduced the so-called bounded workload condition, which requires the workload process be bounded by a free process plus the initial workload. This condition is for a derived process, the workload, as opposed to primitives such as arrival processes and service requirements; as such, it could be difficult to verify. In this paper, we establish the interchange of limits under a moment condition of suitable order on the primitives directly: the required order is p∗>2(p+2) on the moments of the primitive processes so as to bound the pth moment of the workload. This moment condition is trivial to verify, and indeed automatically holds in networks where the primitives have moments of all orders, for instance, renewal arrivals with phase-type interarrival times and independent and identically distributed phase-type service times. | Keywords: | Resource-sharing network Diffusion limit Stationary distribution Interchange of limits Uniform stability |
Publisher: | Institute for Operations Research and the Management Sciences | Journal: | Mathematics of operations research | ISSN: | 0364-765X | EISSN: | 1526-5471 | DOI: | 10.1287/moor.2020.1065 | Rights: | © 2021, INFORMS This is a post-peer-review, pre-copyedit version of an article published in Mathematics of Operations Research. The final authenticated version is available online at: https://doi.org/10.1287/moor.2020.1065. |
| Appears in Collections: | Journal/Magazine Article |
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| Ye_Fair_Resource_Control.pdf | Pre-Published version | 1.02 MB | Adobe PDF | View/Open |
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