In this paper we apply routing algorithms in circuit switched networks to B-ISDN networks and investigate the performance. B-ISDN supports a wide range of services with hetrogeneous bandwidth requirements. We assume that the network supports D classes of traffic. It is modeled as a finite D dimensional Markov chain. A call is blocked on arrival if the required bandwidth is not available on the route. The shortest path routing, alternate routing and trunk reservation are considered for performance comparison. We also consider trunk reservation with restricted access control where the network reserves certain amount of bandwidths for one class of traffic that assumes a higher transmission priority. Through the method of successive iterations, we obtain the steady state equilibrium probabilities and call blocking probabilities for dynamic routing. The results can be used to design a B-ISDN network that improves network connection availability and efficiency while simultaneously reducing the network costs.