Increasing convergence among heterogeneous radio networks is expected to be a key feature of future ubiquitous services. The convergence of radio networks in combination with dynamic spectrum allocation (DSA) could be a beneficial means to solve the growing demand for radio spectrum. DSA might enhance the spectrum utilization of involved radio networks to comply with user requirements for high-quality multimedia services. This paper proposes a simple spectrum allocation algorithm and presents an analytical model of dynamic spectrum resource allocation between two networks using a 4-D Markov chain. We argue that there may exist a break-even point for choosing whether or not to adopt DSA in a system. We point out certain circumstances where DSA is not a viable alternative. We also discuss the performance of DSA against the degree of resource sharing using the proposed analytical model and simulations. The presented analytical model is not restricted to DSA, and can be applied to a general resource sharing study.