Call center data modeling: a queueing science approach based on Markovian arrival process

In this paper we analyze the well-known ‘Anonymous bank’ call center dataset from a queueing science viewpoint. For this purpose, fitted distributions for both the inter-arrival and service times as well as for customers patiences are integrated in a simulator to infer quantities of interest related to call centers managerial decisions as waiting times, abandonment rates and queue lengths. In particular, it is shown how a type of Markov renewal process, the Markovian arrival process (<i>MAP</i>), is able to capture some of the characterizing properties of arrivals in a modern call center as overdispersion and positive correlation between arrival counts. The work provides a new inference approach for the <i>MAP</i> based on the count process descriptors and presents new properties concerning the dependence structure of the cumulated number of arrivals in a <i>MAP</i>.

本文从排队科学的视角，对广为人知的“匿名银行”呼叫中心数据集展开分析。为此，我们将到达间隔时间、服务时长以及顾客耐心度的拟合分布集成至仿真器中，以此推导出与呼叫中心管理决策相关的关键量化指标，包括等待时长、弃线率与队列长度。具体而言，本文阐明了一类马尔可夫更新过程——马尔可夫到达过程（Markovian Arrival Process，MAP）——如何能够捕捉现代呼叫中心到达过程的部分核心特征，例如过度离散特性与到达计数间的正相关性。本研究提出了一种基于计数过程描述符的MAP全新推断方法，并揭示了MAP中累计到达数的依赖结构相关的新性质。