I developed the cpsurvsim R package to
provide functionality for simluating time-to-event data from the
exponential (or piecewise constant) hazard function and the Weibull
hazard function using two different simulation methods (using the
inverse CDF and a memoryless approach). You can find the package on CRAN here. My
forthcoming paper in The R Journal compares the performance of these
methods through a simulation study while encouraging users to determine
which method is best for their data, as I found in my own research there
are scenarios where the memoryless method generates data that more
closely matches your simulation parameters, even though the inverse CDF
approach appears to perform better overall in these simulations.