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Title: Diffusion approximation for fair resource control - interchange of limits under a moment condition
Authors: Ye, H-Q 
Yao, DD
Issue Date: 2021
Source: Mathematics of operations research, Published Online:21 Apr 2021, Ahead of Print, p. 1-26, https://doi.org/10.1287/moor.2020.1065
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.
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