An analysis of the number of tasks in a parallel multi-processor system with task-splitting and feedback

In this paper we have analyzed a parallel multi-processor system with task-splitting and feedback. The explicit time-dependent distribution of the number of tasks in the system is obtained for the single-processor. This distribution is also found for the multi-processor case in which a processed task can not exit the system before going for splitting. The explicit closed form distributions and the means are also obtained for the steady-state cases. For the system in general, the Laplace transform of time-dependent distribution of the number of tasks in the system is found. For the system with a finite buffer, explicit time-dependent and steady-state distribution of the number of tasks in the system are advanced. Numerical examples are given to illustrate the workability of the results.