In a cognitive wireless network, sudden arrival of a primary user could force one or more secondary users to terminate their ongoing communication. This situation leads us to propose a cognitive wireless network which dynamically assigns service rates to the secondary users depending on the available network spectral resource. Our analysis is based on a two-dimensional Markov chain with three state variables. Performance metrics for the secondary users such as dropping probability, blocking probability and completion probability are derived. Our numerical result demonstrates that, depending on the network condition, the proposed dynamic spectrum assignment scheme is capable of reducing the dropping probability substantially and yielding higher throughput via increasing the maximum allowable service rate. Analysis of blocking probability implies that higher value of the maximum allowable service rate may or may not make the network more selective in terms of admitting new secondary users.