IEOR 6707: Advanced Topics in Queueing Theory:
Focus on Customer Contact Centers

Time and Place: 11:00am-12:15pm on Mondays in 825 Mudd and 2:40-3:55pm on Thursdays in 253 Engineering Terrace

Office hours: 529 Mudd, after class and by appointment; email: ward.whitt @columbia.edu

• This course is a research course, giving students the opportunity to conduct independent research. That goal makes it possible for students to participate with a variety of backgrounds. The main task is a course project, which can be conducted individually or in small groups. The course project will culminate in both a written report and an oral presentation. The instructor will suggest possible projects, but students choose their own project. There will be lectures and homework in the first part of the course, and then student project presentations at the end of the course. There will be no exams.

• The course is primarily an advanced doctoral course, being a sequel to the first-year doctoral courses, IEOR 6711 and IEOR 6712, Stochastic Models I and II, and also the graduate course on queueing theory, IEOR 6704. (IEOR 6704 was taught by Professor Sigman in Spring 2004.) That course focused on single-server queues. In contrast, this course will focus on multi-server queues. Even though IEOR 6704 will be very helpful background, it is not a prerequisite.

• The lectures at the beginning will focus on mathematical models and mathematical analysis of those models. To benefit from those lectures, some background is needed in the theory of probability and stochastic processes, but interesting research can be done without much background. However, it is expected that most students will have completed the first-year doctoral courses, IEOR 6711 and IEOR 6712, Stochastic Models I and II, and perhaps also the graduate course on queueing theory, IEOR 6704. However, perhaps it is sufficient to have completed the undergraduate courses IEOR 3600 (Introduction to Probability) and IEOR 3106/4106 (Introduction to Stochastic Models), or the equivalent. Even that may not be necessary, but some probability background is essential.

• This course will focus on stochastic models of customer contact centers. One goal is to help students learn about that application context. (The instructor has some genuine experience.) A second goal is to focus on a class of mathematical models and analysis techniques that have proven useful in that application context. As is almost always the case in operations research, these models and analysis techniques have many other applications, so that the course can be useful even if you are primarily interested in other applications.

• From the mathematical perspective, the course focuses on multi-server queues, with and without additional waiting space, and networks of such multi-server queues. Important customer behavior includes balking (deciding upon arrival not to wait), reneging or abandoning (leaving after waiting a while) and retrying (coming back later after balking or reneging). There may be multiple types of customers and customer service representatives (agents) with different sets of skills. Automatic call distributors provide the capability of skill-based routing, but there remains an opportunity to improve the routing.

• As the author has been doing for almost 40 years, and as is consistent with recent research on contact centers, we will pay special attention to heavy-traffic stochastic-process limits. In particular, here we will focus on the many-server heavy-traffic limits for multi-server queues, in which both the arrival rate and the number of servers approach infinity. Three different limiting regimes emerge, depending on the way these variables approach infinity: (i) the quality-driven (QD) regime, (ii) the efficiency-driven (ED) regime and (iii) the quality-and-efficiency-driven (QED) regime.

• A second major topic in the course will be numerical transform inversion, which has been one of the instructor's main research areas for the last twenty years.

• Other topics include: time-dependent arrival rates, offered-load (infinite-server) models, overflow processes, skill-based routing, staffing, resource pooling, real-time congestion prediction, demand forecasting and simulation.

• Generally, the course is intended to enhance the student's ability to work with stochastic models. More specifically, it is intended to help students be able to effectively conduct research on stochastic models. And, even more specifically, the course is intended to prepare the student to conduct research on customer contact centers and related service systems.

Text: Brad Cleveland and Julia Mayben,
Call Center Management On Fast Forward, Succeeding in Today's Dynamic Inbound Environment,

• This is a leading professional trade publication on the management of customer contact centers that interact with customers through incoming telephone calls. It gives a nice feel for call centers. It shows the relevance of stochastic models, but it also gives a broader perspective. It is readable, sensible and inexpensive. It is intended to provide background on context to supplement the more mathematical focus of the course. Do not judge the mathematical level of the course by this book!

Overview Papers

• N. Gans, G. Koole and A. Mandelbaum, "Telephone call centers: tutorial, review and research prospects," Manufacturing and Service Operations Management, vol. 5, 2003, 79--141. PDF

• W. Whitt, "Stochastic models for the design and management of customer contact centers: some research directions," March 2002. Postscipt PDF

Background Introductory Queueing Textbooks (not required)

• R. B. Cooper, Introduction to Queueing Theory, second edition, North Holland, 1981. On reserve. Out of print, but available in .pdf format (about 13mb zipped) from Michael Taaffe at VPI, with approval from the author.

• R. W. Hall, Queueing Methods for Service and Manufacturing, Prentice Hall, 1991.

Background on Stochastic-Process Limits (not required)

• W. Whitt, Stochastic-Process Limits, Springer, 2002.

Initial Lecture Topics

Possible Project Topics

Related Links for Customer Contact Centers

Research Papers

• My research papers on customer contact centers and multiserver queues