The decision model of task allocation for constrained stochastic distributed systems

In distributed systems, an application program is divided into several software modules, which need to be allocated to processors connected by communication links. The distributed system reliability (DSR) could be defined as the probability of successfully completing the distributed program. Previous studies about optimal task allocation with respect to DSR focused on the effects of the inter-connectivity of processors, the failure rates of the processors, and the failure rates of the communication links. We are the first to study the effects of module software reliabilities and module execution frequencies on the optimal task allocation. By viewing each module as a state in the Markov process, we build a task allocation decision model to maximize DSR for distributed systems with 100% reliable network. In this model, the DSR is derived from the module software reliabilities, the processor hardware reliabilities, the transition probabilities between modules, and the task allocation matrix. Resource constraints of memory space limitation and computation load limitation on each processor are considered. The constraint of total system cost, including the execution cost, the communication cost, and the failure cost, is also considered. We solve the problem by Constraint Programming using the ILOG SOLVER library. We then apply the proposed model to a case extended from previous studies. Finally, a sensitivity analysis is performed to verify the effects of module software reliabilities and processor hardware reliabilities on the DSR and on the task allocation decision.