Telephone Call Centers - Performance, Design and Control of Time Varying Queues

本研究计划旨在研究四个具体领域：(1)呼叫中心逗留时间分布分析；(2)呼叫中心建模；(3)为缓冲区有限、客户缺乏耐心的呼叫中心配备服务人员；(4)一些马尔可夫服务网络模型的非高斯扩散限制下的服务器配置。通过其渐近分析开发的时变排队模型是由为呼叫中心创建操作分析的愿望指导的。研究结果将解决这些系统的性能、设计和控制等基本问题。这些方法的一个最终目标是创建新的简化算法，供从业者使用。这些新的数学技术将增加对时间依赖行为的理解，并为创建新型呼叫中心提供工具。我们需要新的“经验法则”公式和算法来应对这些挑战。为更广泛的排队模型类开发更深入的分析是提供这种见解的重要方法。主要企业和客户之间的大部分互动都是通过呼叫中心的沟通媒介进行的。这种信息的传递通过增加产品的销售和获得必要的反馈来更好地响应客户的需求，从而帮助企业繁荣发展。因此，呼叫中心的增长是由新业务的增长、旧业务的扩张以及信息技术的速度、容量和成本驱动的。呼叫中心运营成本的近三分之二涉及人员问题。因此，任何优化呼叫中心人员配置的方法都对企业的有效管理产生重大影响。传统上，排队理论一直是服务系统设计和运行的重要工具。然而，这些传统的排队模型并没有开始描述在现实世界呼叫中心复杂性中发现的所有详细属性。这样的系统很容易具有随时间变化的代理数量、不同类型的客户需求和代理的多种技能集。这些特点都表明，需要为呼叫中心的操作设计、性能和控制开发更丰富的可处理队列模型。

This research plan aims to investigate four specific areas: (1) the analysis of sojourn time distributions for call centers; (2) the modelling of contact centers; (3) server staffing for call centers with finite buffers and impatient customers; and (4) server staffing with non-Gaussian diffusion limits for some Markovian service network models. The time varying queueing models to be developed through their asymptotic analysis are guided by a desire to create an operational analysis for call centers. The results will address the fundamental problems of performance, design and control for these systems. One ultimate goal of the methods is to create new simplifying algorithms that practitioners can use. These new mathematical techniques will increase the understanding of time-dependent behavior and give tools for creating new types of call centers. New "rule of thumb" formulas and algorithms are needed for these challenges. Developing a deeper analysis for a broader class of queueing models becomes an important way to provide this insight. The majority of interactions between major businesses and their customers happens through the communication medium of call centers. This transfer of information helps businesses prosper by increasing the sales of their products and getting the necessary feedback to be more responsive to customer needs. Thus, the growth of call centers is driven by the growth of new businesses, the expansion of old ones, as well as the speed, capacity and cost of information technology. Nearly two-thirds of the cost for running call centers involves issues of staffing. Hence any methodology that optimizes the staffing of call centers has a significant impact on the efficient management of businesses. Traditionally queueing theory has been an important tool in the design and performance of service systems. However, these traditional queueing models do not begin to describe all the detailed attributes found in the real world complexity of call centers. Such systems can easily have time varying numbers agents, heterogeneous types of customers needs and multiple skill sets for agents. Each of these features points to a need to develop a richer class of tractable queueing models for the operational design, performance and control of call centers.