Cognitive radio presents a new approach to wireless spectrum utilization and management. In this work, the potential performance improvement gained by applying cognitive radio to wireless mesh networks is investigated. Specifically, the potential benefits in terms of QoS provided to users and the efficiency of resource utilization are quantified in a system consisting of a collection of one or more service provider wireless networks. To achieve this, we formulate the problem mathematically using integer linear programming. It is shown that the cognitive radio abilities provide an advantage over the classical network, either by improving QoS through increasing the probability of accepting connection requests, or by reducing the resources needed to fulfill the QoS requirements of users. This advantage is gained without impacting the service of primary clients. More importantly, we show that virtual wireless networks can be created, utilizing only the residual wasted bandwidth of the primary service providers. These virtual networks are able to support large volumes of users, while still ensuring that QoS reliability requirements, such as acceptance probability guarantees, are achieved.