Optimal task partition and state-dependent loading in heterogeneous two-element work sharing system

Many real-world systems such as multi-channel data communication, multi-path flow transmission and multi-processor computing systems have work sharing attributes where system elements perform different portions of the same task simultaneously. Motivated by these applications, this paper models a heterogeneous work-sharing system with two non-repairable elements. When one element fails, the other element takes over the uncompleted task of the failed element upon finishing its own part; the load level of the remaining operating element can change at the time of the failure, which further affects its performance, failure behavior and operation cost. Considering these dynamics, mission success probability (MSP), expected mission completion time (EMCT) and expected cost of successful mission (ECSM) are first derived. Further, optimization problems are formulated and solved, which find optimal task partition and element load levels maximizing MSP, minimizing EMCT or minimizing ECSM. Effects of element reliability, performance, operation cost on the optimal solutions are also investigated through examples. Results of this work can facilitate a tradeoff analysis of different mission performance indices for heterogeneous work-sharing systems.