As more and more services with definite QoS requirements go into the Internet

ISP's face a severe challenge that how maximum number of users can be admitted into networks with QoS guarantees.In this paper

a mathematical model is built first for describing the problem of optimum network resource allocation.Secondly

it is proved that the problem above can be simplified into an easy optimization programming

the unique optimal solution to which is just that of the original problem

and whose optimal value is the upper bound of the number of admitted users.At last

a novel path level network resource allocation algorithm

ERA algorithm

is developed based on the characteristics of that optimal solution.The ERA algorithm possesses the good simplicity and efficiency

and the numerical results also show that it outperforms other algorithms dealing with the same problem.