Load Balancing Scheduling for Batch-Ordered Job-Store: Online vs. Offline

Efficient resource utilization is crucial in real-world applications, especially for balancing loads across machines handling specific job types. This paper introduces a novel batch-ordered job-store scheduling model, where jobs in a batch are scheduled sequentially, with their operations allocated in a round-robin fashion across two scenarios. We establish that this problem is NP-hard and analyze it in both online and offline settings. In the online case, we first examine the exclusive scenario, where operations within the same job must be scheduled on different machines, and show that a load greedy (LG) algorithm achieves a tight competitive ratio of $2-\frac{1}{m}$, with $m$ representing the number of machines. Next, we consider the circular scenario, which requires maintaining the circular order of operations across ordered machines. In this context, we analyze potential anomalies in load distribution during local optimality achieved by the ordered load greedy (OLG) algorithm and provide bounds on the occurrence of these anomalies and the maximum load in each local scheduling round. In the offline case, we abstract each OLG scheduling process as a generalized circular sequence alignment (CSA) problem and develop a dynamic programming-based matching (DPM) algorithm to solve it. To further enhance load balancing, we develop a dynamic programming-based optimization (DPO) algorithm to schedule multiple jobs simultaneously in both scenarios. Experimental results confirm the efficiency of DPM for the CSA problem, and we validate the load balancing effectiveness of both online and offline algorithms using real traffic datasets. These theoretical findings and algorithmic implementations lay a solid groundwork for future practical advancements.