Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.

Access Point Association Coordination in Densely Deployed 802.11 Wireless Networks

Dense deployment of wireless local area network (WLAN) access points (APs) is an important part of the next generation Wi-Fi and standardization (802.11ax) efforts are underway. Increasing demand for WLAN connectivity motivates such dense deployments, especially in geographical areas with large numbers of users, such as stadiums, large enterprises, multi-tenant buildings, and urban cities. Although densification of WLAN APs guarantees coverage, it is susceptible to increased interference and uncoordinated association of stations (STAs) to APs, which degrade network throughput. Therefore, to improve network throughput, algorithms are proposed in this thesis to optimally coordinate AP associations in the presence of interference. In essence, coordination of APs in dense WLANs (DWLANs) is achieved through coordination of STAs' associations with APs. While existing approaches suggest tuning of APs' beacon powers or using transmit power control (TPC) for association control, here, the signal-to-interference-plus-noise ratio (SINRs) of STAs and the clear channel assessment (CCA) threshold of the 802.11 MAC protocol are employed. The proposed algorithms in this thesis enhance throughput and minimize coverage holes inherent in cell breathing and TPC techniques by not altering the transmit powers of APs, which determine cell coverage. Besides uncoordinated AP associations, unnecessary frequent transmission deferment is envisaged as another problem in DWLANs due to the clear channel assessment aspect of the carrier sensing multiple access collision avoidance (CSMA/CA) scheme in 802.11 standards and the short spatial reuse distance between co-channel APs. To address this problem in addition to AP association coordination, an algorithm is proposed for CCA threshold adjustment in each AP cell, such that CCA threshold used in one cell mitigates transmission deferment in neighboring cells. Performance evaluation reveals that the proposed association optimization algorithms achieve significant gain in throughput when compared with the default strongest signal first (SSF) association scheme in the current 802.11 standard. Also, further gain in throughput is observed when the CCA threshold adjustment is combined with the optimized association. Results show that when STA-AP association is optimized and CCA threshold is adjusted in each cell, throughput improves. Finally, transmission delay and the number of packet re-transmissions due to collision and contention significantly decrease.