Some real-time systems consist of a number of processes that operate under age constraints. In such systems, the maximum time from the start of process L-i in cycle k to the end in cycle k+1 must not exceed the age constraint A(i) for that process. The age constraint can be met by using fixed priority scheduling and periods equal to A(i)/2. However, this approach restricts the number of process sets which are schedulable. In this paper, we define a method for obtaining process periods other than A(i)/2. The periods are calculated in such a way that the age constraints are met. Our approach is better in the sense that a larger number of process sets can be scheduled compared to using periods equal to A(i)/2. The main results in this paper are a number of performance bounds on age constraint processes. These bounds show that there is a significant gain in worst case as well as in best case behavior by using periods other than A(i)/2, particularly when there are a large number of processes in the system.