This dissertation is based on a traditional circuit switched core WDM network that is supplemented by a pool of wavelengths that carry optical burst switched overflow data. These overflow channels function to absorb channel overflows from traditional circuit switched networks and they also provide wavelengths for newer, high bandwidth applications. The channel overflows that appear at the overflow layer as optical bursts are either carried over a permanently configured, primary light path, or over a burst-switched, best-effort path while traversing the core network. At every successive hop along the best effort path, the optical bursts will attempt to enter a primary light path to its destination. Thus, each node in the network is a Hybrid Node that will provide entry for optical bursts to hybrid path that is made of a point to point, pre-provisioned light path or a burst switched path. The dissertation's main outcome is to determine the cost optimality of a Hybrid Route, to analyze cost-effectiveness of a Hybrid Node and compare it to a route and a node performing non-hybrid operation, respectively. Finally, an example network that consists of several Hybrid Routes and Hybrid Nodes is analyzed for its cost-effectiveness. Cost-effectiveness and optimality of a Hybrid Route is tested for its dependency on the mean and variance of channel demands offered to the route, the number of sources sharing the route, and the relative cost of a primary and overflow path called path cost ratio. An optimality condition that relates the effect of traffic statistics to the path cost ratio is analytically derived and tested. Cost-effectiveness of a Hybrid Node is compared among different switching fabric architecture that is used to construct the Hybrid Node. Broadcast-Select, Benes and Clos architectures are each considered with different degrees of chip integration. An example Hybrid Network that consists of several Hybrid Routes and Hybrid Nodes is found to be cost-effective and dependent of the ratio of switching to transport costs.