Effective project management requires accurate estimation and management of the project timeline and simulation provides a way for project managers to quickly determine the overall critical-path of activities and the earliest completion date.  However, many project simulations use arbitrarily chosen probability distributions to model individual task durations.  This paper investigates the sensitivity of Monte Carlo simulation outcomes to the selection of task duration distributions. The study compares standard functions such as Triangular Normal, Lognormal, Gamma, and Beta distributions to assess their impact on project completion estimates.

Parallel tasks pose a higher risk to project deadlines than more linear task structures.  A network of up to twenty tasks with identical precedence and dependency constraints was modeled with task parameters normalized to ensure mean-equivalence across all distributions.  Individual task durations were simulated through the use of the output of a random number generator input into the inverse cumulative distribution functions of the aforementioned distributions.  Through 10,000 simulation iterations per scenario, the divergences in the mean, median, and standard deviation of the total project duration were analyzed.  Histograms of total project durations for each simulation were generated to visualize the completion profile produced by each distribution.  These results were verified analytically and presented in an easily repeatable way for project management practitioners for use in projects with simple parallel task structures.

The compounding effect created by highly parallel critical-path networks were found to create a strong late-bias in the cumulative final durations of projects with right biased triangular and beta task duration probability distributions.  Early task completion times with these distributions in highly parallel task structures were found to result in later than mid-range project completion performance.  The long tail distributions of normal, lognormal, and gamma distributed tasks were found to be exaggerated by highly parallel task structures, which amplified variability of completion times with those projects.