高负荷服务下双端排队系统的扩散近似
Diffusion Approximations for Double-ended Queues with Reneging in Heavy Traffic
摘要：
研究了由两类顾客组成的双端排队系统。只要有一对来自两个类的客户，它们就会被匹配并立即离开系统。比赛遵循先到先得的原则。如果来自一个类的客户不能立即匹配，他/她将留在队列中，等待来自另一个类的即将到来的到来。因此，在系统中不可能同时有来自两个类别的非零数量的客户。我们还假设每个客户都可以离开队列，而不会因为不耐烦而被匹配。假设到达过程是独立的更新过程，并且两类的耐心时间一般都是分布的。在适当的高负荷服务条件下，假设扩散标度队列长度过程是随机有界的，建立了扩散标度队列长度过程与扩散标度提供等待时间过程之间的一个简单的渐近关系，并进一步证明了扩散标度队列长度过程弱收敛于一个扩散过程.我们还提供了一个充分条件的随机有界的扩散标度的队列长度过程。最后给出了极限扩散过程平稳分布的显式表达式。
英文摘要：
We study a double-ended queue which consists of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system immediately. The matching follows first-come-first-serve principle. If a customer from one class cannot be matched immediately, he/she will stay in a queue and wait for the upcoming arrivals from the other class. Thus there cannot be non-zero numbers of customers from both classes simultaneously in the system. We also assume that each customer can leave the queue without being matched because of impatience. The arrival processes are assumed to be independent renewal processes, and the patience times for both classes are generally distributed. Under suitable heavy traffic conditions, assuming that the diffusion-scaled queue length process is stochastically bounded, we establish a simple asymptotic relationship between the diffusion-scaled queue length process and the diffusion-scaled offered waiting time process, and further show that the diffusion-scaled queue length process converges weakly to a diffusion process. We also provide a sufficient condition for the stochastic boundedness of the diffusion-scaled queue length process. At last, the explicit form of the stationary distribution of the limit diffusion process is derived.
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。
