Mathematical modeling and analysis of wireless mesh network scheduling

Abstract

Due to the increasing demand for high-speed Internet access, wireless mesh networks (WMN) have become a popular choice for their ease of deployment and ubiquity. Although extensive research has been done in the literature regarding WMNs, almost all approaches rely on simulations and there is a lack of focus on analytical approach and mathematical modeling. In this thesis, a novel mathematical model called the "Bosphorus Boat Model" (BoBo) is proposed for the mathematical modeling of scheduling on infrastructure-based WMNs. Probability distributions regarding the queue occupancy at di erent points in time are derived. Not only are these distributions used for deriving important metrics for evaluation and veri cation, but also their behavior is investigated for a thorough analysis. The evaluation of the BoBo model is also veri ed with simulations. The results show that the probability distribution of queue occupancy at any given point in time resembles the normal distribution, and increasing tra c load induces an increase in variance. Also, the number of frame to which a packet is scheduled has an almost deterministic distribution with very low variance. However, under the condition of reaching network capacity, the distribution becomes almost equiprobable for the two-hop nodes.