A method for forecasting time delays added to a scheduled start time and a scheduled end time of a task includes generating a stochastic model of the task and resources affecting the task, the stochastic model includes a reactionary delay component that is a function of previous task end times and a root cause delay component that is an independent random process at a specific time. The method further includes: calculating a probability distribution of time delays added to the scheduled start time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of start times; and calculating a probability distribution of time delays added to the scheduled end time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of end times.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. (canceled) 2. (canceled) 3. (canceled) 4. (canceled) 5. (canceled) 6. (canceled) 7. (canceled) 8. (canceled) 9. (canceled) 10. (canceled) 11. (canceled) 12. (canceled) 13. (canceled) 14. (canceled) 15. A system for forecasting time delays added to a scheduled start time and a scheduled end time of a task, the system comprising: a processor configured to: generate a stochastic model of the task and resources affecting the task, the stochastic model comprising a reactionary delay component and a root cause delay component, the reactionary component being a function of previous task end times and the root cause delay component being an independent random process at a specific time; calculate a probability distribution of time delays added to the scheduled start time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of start times; calculate a probability distribution of time delays added to the scheduled end time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of end times; transmit a signal comprising the probability distribution of start times and the probability distribution of end times to a signal receiving device; a signal receiving device configured to receive the signal comprising the probability distribution of start times and the probability distribution of end times. 16. The system according to claim 15, wherein the signal receiving device comprises at least one of a display and a printer. 17. The system according to claim 15, wherein the signal receiving device comprises at least one of a non-transitory storage medium and memory. 18. The system according to claim 15, wherein the stochastic model is a hidden Markov model (HMM) and the processor is further configured to train the HMM using historical schedule and delay data. 19. The system according to claim 15, wherein the processor is further configured to: generate a stochastic model of each of the sub-tasks and resources affecting the sub-tasks, the stochastic model comprising a reactionary delay component and a root-cause delay component, the reactionary delay component being a function of previous sub-task end times and the root-cause delay component being an independent random process at a specific time; calculate a probability distribution of time delays added to a scheduled start time of each sub-task as a combination of the reactionary delay component and the root cause delay component of each sub-task using the stochastic model of each of the sub-tasks and resources affecting the sub-tasks to provide a probability distribution of start times of the sub-tasks; and calculate a probability distribution of time delays added to a scheduled end time of each sub-task as a combination of the reactionary delay component and the root cause delay component of each sub-task using the stochastic model of each of the sub-tasks and resources affecting the sub-tasks to provide a probability distribution of end times of the sub-tasks. 20. A non-transitory computer-readable medium comprising computer-executable instructions for forecasting time delays added to a scheduled start time and a scheduled end time of a task that when executed by a computer implement a method comprising: generating a stochastic model of the task and resources affecting the task, the stochastic model comprising a reactionary delay component and a root cause delay component, the reactionary component being a function of previous task end times and the root cause delay component being an independent random process at a specific time; calculating a probability distribution of time delays added to the scheduled start time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of start times; calculating a probability distribution of time delays added to the scheduled end time as a combination of the reactionary delay component and the root cause delay component using the stochastic model to provide a probability distribution of end times; and transmitting a signal comprising the probability distribution of start times and the probability distribution of end times to a signal receiving device.