Queues with Customer Abandonment and Stochastic Fluid Flow processes

具有顾客遗弃、恒定/随机不耐烦时间和许多服务生的排队是流行的随机模型，在呼叫中心的设计等领域有着广泛的应用。尽管这样的队列已经被研究人员和从业者广泛调查，但在新的应用程序中出现了一些需要探索的问题。*在本研究中，我们关注两类问题。1)准确分析丢弃客户和多台服务器的排队情况。在现有文献中，大多数关于顾客遗弃排队的研究都是基于扩散过程和大偏差等近似方法。需要对轻交通中的这类排队进行精确的分析，这对于此类随机系统的设计是非常重要的。2)数据驱动的顾客放弃排队分析。在考虑顾客遗弃的排队设计中，遗弃率起着关键作用。我们计划提出基于等待时间和队列长度等系统信息来估计丢弃率的方法。然后，我们使用估计的丢弃率来分析/设计这样的排队系统。*我们将在研究中使用和推广两套技术工具。I)首先，我们将使用矩阵分析方法(MAM)对感兴趣的队列进行精确分析。MAM由一组工具组成，这些工具在排队、可靠性系统和供应链等随机模型的分析中被广泛使用。这些方法不仅产生了对随机系统的精确分析，而且还产生了计算性能度量/量的有效算法。Ii)其次，我们将使用随机流体流动过程来研究具有顾客遗弃的排队。我们将为我们的排队模型引入适当的流体流动过程，然后开发研究流体流动过程的方法。此外，我们计划将我们的研究扩展到与矩阵分析方法和流体流动过程有密切关系的风险/保险模型。*本研究的成果包括对顾客遗弃排队模型的精确分析和新的求解方法的发展，这些方法可用于随机系统的设计。拟议的研究涉及使用两套工具来调查一些随机模型，这些模型适合培养学生掌握随机建模、数据分析和优化的技能，并为他们未来的职业生涯做好准备。该研究在电信业(如呼叫中心设计)、服务业(如银行系统设计)、制造/物流系统(如供应链设计)和金融业(如风险和保险分析)等行业具有潜在的应用价值。我们将找到真实/实际的案例来验证本研究中使用的方法，并举例说明我们的研究。

Queues with customer abandonment, constant/stochastic impatient time, and many servers are popular stochastic models with applications in a number of areas such as the design of call centers. Although such queues have been investigated extensively by researchers and practitioners alike, there are issues arisen in new applications that require exploration. ******In this research, we focus on two types of problems. 1) Exact analysis of queues with customer abandonment and many servers. In the existing literature, the majority of studies on queues with customer abandonment are based on approximation methods such as diffusion processes and large deviation. There is a need for an exact analysis of such queues in light traffic, which is of significant importance to the design of such stochastic systems. 2) Data driven analysis of queues with customer abandonment. In the design of queues with customer abandonment, abandonment rate plays a key role. We plan to propose methods to estimate the abandonment rate based on system information such as waiting time and queue length. Then we use the estimated abandonment rate in the analysis/design of such queueing systems. *** ***We shall use and extend two sets of technical tools in the research. i) First, we shall use matrix-analytic methods (MAM) to conduct an exact analysis of the queues of interest. MAM consists of a set of tools that have been used extensively in the analysis of stochastic models such as queues, reliability systems, and supply chains. Those methods not only generate exact analyses of stochastic systems, but also lead to efficient algorithms for computing performance measures/quantities. ii) Second, we shall use stochastic fluid flow processes in the study of queues with customer abandonment. We shall introduce proper fluid flow processes for our queueing models and then develop methods to investigate the fluid flow processes. In addition, we plan to extend our study to risk/insurance models, which have a close relationship with matrix-analytic methods and fluid flow processes. ******The outcomes of this research include the exact analysis of queueing models with customer abandonment and the development of new solution methods, which can be used in the design of stochastic systems. The proposed research involves the use of two sets of tools to investigate a number of stochastic models, which are suitable for training students to master skills in stochastic modeling, data analytics, and optimization, and preparing them for their future careers. The research has potential applications in several industries such as telecommunications industry (e.g., design of call centers), service industry (e.g., design of banking systems), manufacturing/logistic systems (e.g., design of supply chains), and finance industry (e.g., risk and insurance analysis). We shall find real/practical cases to validate the methods used in this research and to exemplify our research.