标题： 如何在工人士气低落的系统中最大化效率 显示英文标题

标题： How to Maximize Efficiency in Systems with Exhausted Workers

摘要： 我们考虑将任务高效分配给一组工人的问题，这些工人可能会因为处理任务而精疲力竭。如果一个工人精疲力竭，它需要更长的时间来恢复。为了建模带精疲力竭的工人的效率，我们使用连续时间马尔可夫链（CTMC）。通过从工人的内部状态采样，当源发现工人处于高效状态时，为其分配任务。我们考虑两种不同的情况：(i) 源只能在工人处于最高效状态时为其分配任务；(ii) 即使成功概率可能降低，源也可以在工人也处于中等效率状态时为其分配任务。在前者情况下，我们发现最优策略是一种基于阈值的采样策略，其中阈值依赖于工人的恢复和精疲力竭率。在后者情况下，我们使用分支定界方法解决了一个非凸比率和问题，该方法的表现优于全局最优解。 显示英文摘要

摘要： We consider the problem of assigning tasks efficiently to a set of workers that can exhaust themselves as a result of processing tasks. If a worker is exhausted, it will take a longer time to recover. To model efficiency of workers with exhaustion, we use a continuous-time Markov chain (CTMC). By taking samples from the internal states of the workers, the source assigns tasks to the workers when they are found to be in their efficient states. We consider two different settings where (i) the source can assign tasks to the workers only when they are in their most efficient state, and (ii) it can assign tasks to workers when they are also moderately efficient in spite of a potentially reduced success probability. In the former case, we find the optimal policy to be a threshold-based sampling policy where the thresholds depend on the workers' recovery and exhaustion rates. In the latter case, we solve a non-convex sum-of-ratios problem using a branch-and-bound approach which performs well compared with the globally optimal solution.