In this article, we propose a reactive task allocation architecture for a multi-agent system for scenarios where the tasks arrive at random times and are grouped into multiple queues. Two stage tasks are considered where every task has a beginning, an intermediate and a final part, typical in pick-and-drop and inspect-and-report scenarios. A centralized auction-based task allocation system is proposed, where an auction system takes into consideration bids submitted by the agents for individual tasks, current length of the queues and the waiting times of the tasks in the queues to decide on a task allocation strategy. The costs associated with these considerations, along with the constraints of having unique mappings between tasks and agents and constraints on the maximum number of agents that can be assigned to a queue, results in a Linear Integer Program (LIP) that is solved using the SCIP solver. For the scenario where the queue lengths are penalized but not the waiting times, we demonstrate that the auction system allocates tasks in a manner that all the queue lengths become constant, which is termed balancing. For the scenarios where both the costs are considered, we qualitatively analyse the effect of the choice of the relative weights on the resulting task allocation and provide guidelines for the choice of the weights. We present simulation results that illustrate the balanced allocation of tasks and validate the analysis for the trade-off between the costs related to queue lengths and task waiting times.

翻译：本文提出了一种面向多智能体系统的反应式任务分配架构，适用于任务随机到达并被分组至多个队列的场景。研究考虑了包含开始、中间及结束三阶段的两阶段任务（典型场景如“拾取-投放”与“检查-报告”）。我们提出了一种基于集中式拍卖的任务分配系统：该系统综合考虑智能体对单个任务的报价、队列当前长度及队列中任务等待时间，以决策任务分配策略。上述成本指标与任务-智能体唯一映射约束、单队列可分配智能体数量上限约束共同构成线性整数规划问题（LIP），并通过SCIP求解器求解。在仅惩罚队列长度而不涉及等待时间的场景中，我们证明拍卖系统可使所有队列长度收敛至恒定值（即“均衡”状态）。对于同时考虑两类成本的场景，我们定性分析了相对权重选择对任务分配结果的影响，并给出了权重选取建议。仿真结果展示了均衡的任务分配效果，并验证了关于队列长度成本与任务等待时间成本间权衡的分析结论。