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This paper investigates the virtualization and optimization of a multi-cell WLAN. We consider the station (STA)-access point (AP) association and airtime control for virtualized 802.11 networks to provide service customization and fairness across multiple internet service providers (ISPs) sharing the common physical infrastructure and network capacity. More specifically, an optimization problem is formulated on the STAs transmission probabilities to maximize the overall network throughput, while providing airtime usage guarantees for the ISPs. Subsequently, an algorithm to reach the optimal solution is developed by applying monomial approximation and geometric programming iteratively. Based on the proposed three-dimensional Markov-chain model of the enhanced distributed channel access (EDCA) protocol, the detailed implementation of the optimal transmission probability is also discussed. The accuracy of the proposed Markov-chain model and the performance of the developed association and airtime control scheme are evaluated through numerical results.