Ordered balancing: load balancing for redundant task scheduling in robotic network cloud systems

To perform a set of tasks in a robotic network cloud system as fast as possible, it is recommended to use a scheduling approach that minimizes the makespan. The makespan is defined as the time between the start of the first scheduled task and the completion of all scheduled tasks. Load balancing is a technique to distribute incoming tasks across processing units in a way that the resource utilization is optimized and the makespan is minimized. Robotic network cloud systems can be conceptualized as graphs, with nodes representing hardware with independent computing power and edges representing data transmissions between the nodes. The initial scheduler assigns a set of newly arrived tasks to the processing units capable of performing them. To reduce the response time we can replicate some of the tasks and assign them to different processing units. This results in some tasks becoming redundant. Assigning redundant tasks refers to determining which processing unit should receive the replicated tasks. Load balancing for redundant allocation can be viewed as assigning tasks to multiple processing units with different resource sizes so that the load is evenly distributed among the units. We propose a technique for load balancing, the ordered balancing algorithm, to minimize the makespan in the redundant allocation and scheduling problem. We prove theoretically the correctness of the proposed algorithm and illustrate with simulations, using R version 4.0.3, the obtained results that outperform other recent load balancing proposals.