The paper is devoted to modeling wireless mesh networks (WMN) through mixed-integer programming (MIP) formulations that allow to precisely characterize the link data rate capacity and transmission scheduling using the notion of time slots. Such MIP models are formulated for several cases of the modulation and coding schemes (MCS) assignment. We present a general way of solving the max-min fairness (MMF) traffic objective for WMN using the formulated capacity models. Thus the paper combines WMN radio link modeling with a non-standard way of dealing with uncertain traffic, a combination that has not, to our knowledge, been treated so far by exact optimization models. We discuss several ways, including a method based on the so called compatible or independent sets, of solving the arising MIP problems. We also present an extensive numerical study that illustrates the running time efficiency of different solution approaches, and the influence of the MCS selection options and the number of time slots on traffic performance of a WMN. Exact joint optimization modeling of the WMN capacity and the MMF traffic objectives forms the main contribution of the paper.
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