匹配不耐烦且异质的需求与供给
Matching Impatient and Heterogeneous Demand and Supply
AI总结：
针对服务平台异质供需匹配中等待流失与成本问题，构建考虑耐心时间非线性影响的流体模型，推导渐近最优匹配率，提出离散审查及状态无关优先级策略，并揭示指数耐心时间假设的鲁棒性缺陷。
摘要：
服务平台必须制定规则，用于匹配随时间随机到达、若等待匹配时间过长就可能流失的异质需求（客户）和供给（劳动者）。我们的目标是最大化匹配的累计价值，减去需求和供给等待时产生的成本。我们构建了一个流体模型，该模型可近似随机模型的演化过程，并明确捕捉等待的需求与供给数量和其耐心时间（文献中也称为爽约或放弃时间）分布之间的非线性依赖关系。该流体模型的不变量可近似随机系统中的稳态平均队列长度，因此可用于构建一个优化问题，其最优解给出的需求与供给类型间的匹配率是渐近最优的（在流体尺度下，即当需求和供给速率增大时）。我们提出了一种离散审查匹配策略，该策略可渐近实现最优匹配率。我们进一步证明，当上述匹配优化问题存在最优极点解时——该情况出现在耐心时间分布具有递增失效率函数时——一种对连接需求和供给的二部图上的边进行排序的状态无关优先级策略是渐近最优的。该分析的一个关键洞见是，排序结果关键取决于耐心时间分布，即便分布的均值相同，不同分布对应的排序也可能不同，这表明为了易处理性而假设耐心时间服从指数分布的模型可能缺乏鲁棒性。最后，我们发现当持有成本为零时，一种无需知晓到达间隔和耐心时间分布的离散审查策略是渐近最优的。
英文摘要：
Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative value of matches, minus costs incurred when demand and supply wait. We develop a fluid model, that approximates the evolution of the stochastic model, and captures explicitly the nonlinear dependence between the amount of demand and supply waiting and the distribution of their patience times, also known as reneging or abandonment times in the literature. The fluid model invariant states approximate the steady-state mean queue-lengths in the stochastic system, and, therefore, can be used to develop an optimization problem whose optimal solution provides matching rates between demand and supply types that are asymptotically optimal (on fluid scale, as demand and supply rates grow large). We propose a discrete review matching policy that asymptotically achieves the optimal matching rates. We further show that when the aforementioned matching optimization problem has an optimal extreme point solution, which occurs when the patience time distributions have increasing hazard rate functions, a state-independent priority policy, that ranks the edges on the bipartite graph connecting demand and supply, is asymptotically optimal. A key insight from this analysis is that the ranking critically depends on the patience time distributions, and may be different for different distributions even if they have the same mean, demonstrating that models assuming, e.g., exponential patience times for tractability, may lack robustness. Finally, we observe that when holding costs are zero, a discrete review policy, that does not require knowledge of inter-arrival and patience time distributions, is asymptotically optimal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
