论文标题
匹配的队列与匹配的批处理对（M，N）
Matched Queues with Matching Batch Pair (m, n)
论文作者
论文摘要
In this paper, we discuss an interesting but challenging bilateral stochastically matching problem: A more general matched queue with matching batch pair (m, n) and two types (i.e., types A and B) of impatient customers, where the arrivals of A- and B-customers are both Poisson processes, m A-customers and n B-customers are matched as a group which leaves the system immediately, and the customers' impatient behavior is to确保系统的稳定性。我们表明，这种匹配的队列可以表示为一种新型的双向依赖性准直生 - 死亡（QBD）过程。基于此，我们为该匹配的队列提供了详细的分析，包括系统稳定性，平均固定队列长度以及任何A-Customer或B-Customer的平均寄居时间。我们认为，本文开发的方法和结果可用于处理更一般的匹配排队系统，这些系统在各个实际领域都广泛遇到，例如共享经济，乘车平台，双边市场，器官移植，出租车服务，装配系统等。
In this paper, we discuss an interesting but challenging bilateral stochastically matching problem: A more general matched queue with matching batch pair (m, n) and two types (i.e., types A and B) of impatient customers, where the arrivals of A- and B-customers are both Poisson processes, m A-customers and n B-customers are matched as a group which leaves the system immediately, and the customers' impatient behavior is to guarantee the stability of the system. We show that this matched queue can be expressed as a novel bidirectional level-dependent quasi-birth-and-death (QBD) process. Based on this, we provide a detailed analysis for this matched queue, including the system stability, the average stationary queue lengthes, and the average sojourn time of any A-customer or B-customer. We believe that the methodology and results developed in this paper can be applicable to dealing with more general matched queueing systems, which are widely encountered in various practical areas, for example, sharing economy, ridesharing platform, bilateral market, organ transplantation, taxi services, assembly systems, and so on.
