Queues with Customer Abandonment and Stochastic Fluid Flow processes

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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.