Time Warp is an optimistic synchronization protocol used for parallel discrete event simulation. While Time Warp has the potential to reduce the execution time of large simulations, it has been plagued by a variety of problems, namely: 1. Instability due to thrashing effects caused by echoing and cascading rollbacks. 2. Memory bottlenecks due to state saving and excessive optimism. 3. Inefficient scheduling algorithms for scheduling Time Warp processes on each processing node. These problems have inhibited the widespread use of Time Warp as a general purpose synchronization algorithm. The general trend of researchers attempting to solve these problems has been to statically limit the optimism of Time Warp. Unfortunately, these attempts have achieved only limited success. This is because a static set of parameters may perform well for one simulation but not for another. This paper attacks the problem using adaptive mechanisms to control optimism, using an index of performance called useful work. This research presents solutions for the above mentioned problems, by: 1. Stabilizing Time Warp using adaptive bounded time windows. 2. Reducing memory usage and overall execution time by using an adaptive mechanism to vary the checkpoint interval. 3. Scheduling Time Warp processes with the useful work parameter to favor more productive processes. Using this new performance index called Useful Work, several modifications to Time Warp are implemented to stabilize and improve Time Warp. Thus, this new improved Time Warp synchronization mechanism termed Parameterized Time Warp provides an integrated adaptive solution to optimistic Parallel Discrete Event Simulation. Empirical work showing that PTW outperforms an equivalent Time Warp simulation executing under similar partitioning and load conditions is also presented.