论文标题
流量繁忙的多组分匹配队列
Multi-component Matching Queues in Heavy Traffic
论文作者
论文摘要
我们考虑由$ k \ geq 2 $不同的可易腐组成部分组成的繁重流量中的多组分匹配系统，这些组件随着时间的流逝随机到达订单站的高速时随机到达，并且按照匹配或``耐心''的类别等待的类别等待各自的排队等待。 by $n$, we establish an explicit definition for the matching completion process, and when all the arrival rates tend to infinity in concert as $n\to\infty$, we obtain a heavy traffic limit of the appropriately scaled queue lengths under mild assumptions, which is characterized by a coupled stochastic integral equation with a scalar-valued non-linear term. We demonstrate some crucial properties for certain coupled equations and此外，我们建立了一个渐近的小定律，揭示了队列长度及其虚拟等待时间之间的渐近关系。
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues according to their categories until matched or their ``patience" runs out. An instantaneous match occurs if all categories are available, and the matched components leave immediately thereafter. For a sequence of such systems parameterized by $n$, we establish an explicit definition for the matching completion process, and when all the arrival rates tend to infinity in concert as $n\to\infty$, we obtain a heavy traffic limit of the appropriately scaled queue lengths under mild assumptions, which is characterized by a coupled stochastic integral equation with a scalar-valued non-linear term. We demonstrate some crucial properties for certain coupled equations and exhibit numerical case studies. Moreover, we establish an asymptotic Little's law, which reveals the asymptotic relationship between the queue length and its virtual waiting time. Motivated by the cost structure of blood bank drives, we formulate an infinite-horizon discounted cost functional and show that the expected value of this cost functional for the nth system converges to that of the heavy traffic limiting process as n tends to infinity.
