The paper examines the nature of exponential behavior and identifies the conditions under which the probabilistic distribution of the project completion period deviates from the exponential one. For this purpose, a model has been developed in which the evolution of the project is described as a Markov process with a transition matrix containing a constant in all elements of the first row. This structure corresponds to a situation in which the project can be restarted at any time. Project completion times can follow various statistical distributions, including normal, exponential, and more complex forms. Examples of such projects can be research, exploration, venture and other similar projects. An analysis of the dynamics shows that the model reliably reproduces the exponential distribution in cases where the probability of a restart remains moderate. This indicates the limit of applicability of the exponential description.: it is adequate for low and medium restart probabilities, but loses accuracy with a high level of uncertainty.

Keywords: Markov processes, project management, exponential distribution, project completion time, risk assessment, probabilistic forecasting, uncertainty in projects, risks of assumptions, dynamics of project evolution