Admission controllers in dynamic real-time systems perform traditional schedulability tests in order to determine whether incoming tasks will meet their deadlines. These tests are computationally expensive and typically run in n * log n time where n is the number of tasks in the system. An incoming task might therefore miss its deadline while the schedulability test is being performed, when there is a heavy load on the system. In our work we evaluate a new approach for admission control in firm real-time systems. Our work shows that ANNs can be used to perform a schedulability test in order to work as an admission controller in firm real-time systems. By integrating the ANN admission controller to a real-time simulator we show that our approach provides feasible performance compared to a traditional approach. The ANNs are able to make up to 86% correct admission decisions in our simulations and the computational cost of our ANN schedulability test has a constant value independent of the load of the system. Our results also show that the computational cost of a traditional approach increases as a function of n log n where n is the number of tasks in the system.