In this paper two admission control algorithms are defined and evaluated. The algorithms are designed for use with an architecture which segregates traffic flows into multiple queues, one for each individual connection or one for each class of connections. The approach makes it possible to provide multiple classes of service. Resource allocation tables can be prepared efficiently, using simulation. The resulting tables are independent of possible traffic mixtures and require only two scalar numbers to specify required resources. The admission process can be carried out by passing the two numbers between nodes, and it is not necessary to provide detailed information about traffic mixtures. The paper presents a comprehensive performance study, carried out with simulation, to evaluate the performance of the proposed admission control algorithms in relation to other algorithms described in the literature. Under the conditions used in the performance study, simulation is used to establish an admissible region of all possible combinations of the numbers of sources in two classes of traffic which can be supported by a specific channel independent of the admission algorithm. Thus, the algorithms are compared to the best that is possible as well as competing algorithms. For the case of multiple sources with different quality of service requirements, one of the proposed algorithms outperformed three competing algorithms and gave results close to the best that can be achieved with any admission algorithm.