Queues with Customer Abandonment and Stochastic Fluid Flow processes

客户放弃队列、常量/随机等待时间和许多服务器是在呼叫中心设计等许多领域应用的流行随机模型。尽管研究人员和实践者都对这种队列进行了广泛的研究，但在新的应用中出现了一些需要探索的问题。******在本研究中，我们主要关注两类问题。1)准确分析客户弃队和服务器多的队列。在现有文献中，大多数关于顾客放弃队列的研究都是基于扩散过程和大偏差等近似方法。在轻轨交通中，需要对这类队列进行精确的分析，这对设计这类随机系统具有重要意义。2)客户放弃队列的数据驱动分析。在考虑顾客放弃的队列设计中，放弃率起着关键作用。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放弃率的方法。然后，我们将估计的放弃率用于此类排队系统的分析/设计中。*** ***我们将在研究中使用和扩展两套技术工具。i)首先，我们将使用矩阵解析方法（MAM）对感兴趣的队列进行精确分析。MAM由一组工具组成，这些工具已广泛用于分析随机模型，如队列、可靠性系统和供应链。这些方法不仅产生了对随机系统的精确分析，而且还导致了计算性能度量/数量的有效算法。ii)第二，我们将使用随机流体流动过程来研究客户放弃的队列。我们将为我们的排队模型引入适当的流体流动过程，然后发展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解析方法和流体流动过程密切相关的风险/保险模型。******本研究的结果包括对考虑顾客放弃的排队模型的精确分析，并开发了新的求解方法，可用于随机系统的设计。本研究拟采用两套工具对一些随机模型进行研究，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。该研究在电信行业（如呼叫中心的设计）、服务业（如银行系统的设计）、制造业/物流系统（如供应链的设计）和金融业（如风险和保险分析）等多个行业具有潜在的应用前景。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.