Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

A General Framework to Compare Announcement Accuracy: Static vs LES-based Announcement

Service providers often share delay information, in the form of delay announcements, with their customers. In practice, simple delay announcements, such as average waiting times or a weighted average of previously delayed customers, are often used. Our goal in this paper is to gain insight into when such announcements perform well. Specifically, we compare the accuracies of two announcements: (i) a static announcement that does not exploit real-time information about the state of the system and (ii) a dynamic announcement, specifically the last-to-enter-service (LES) announcement, which equals the delay of the last customer to have entered service at the time of the announcement. We propose a novel correlation-based approach that is theoretically appealing because it allows for a comparison of the accuracies of announcements across different queueing models, including multiclass models with a priority service discipline. It is also practically useful because estimating correlations is much easier than fitting an entire queueing model. Using a combination of queueing-theoretic analysis, real-life data analysis, and simulation, we analyze the performance of static and dynamic announcements and derive an appropriate weighted average of the two which we demonstrate has a superior performance using both simulation and data from a call center.

Statistical Analysis of a Telephone Call Center

A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations

Routing and Staffing when Servers are Strategic

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.Comment: First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 201

The influence of information time in the strategic customer behavior

Σε πολλές εφαρμογές οι πελάτες φθάνουν σε ένα σύστημα αναμονής και αποφασίζουν αν θα μπουν σε αυτό η όχι χωρίς να γνωρίζουν το πλήθος των πελατών στο σύστημα. Αργότερα όμως, οι εισερχόμενοι πελάτες ενημερώνονται σχετικά με τον υπολειπόμενο χρόνο αναμονής τους στο σύστημα και τότε μπορούν να αποφασίσουν αν τους συμφέρει να παραμείνουν στο σύστημα ή όχι. Το βασικό ερώτημα που προκύπτει από την παραπάνω περιγραφή είναι κατά πόσο αυτή η καθυστερημένη πληροφορία επηρεάζει τη στρατηγική συμπεριφορά των πελατών. Στο πρώτο μέρος της διπλωματικής εργασίας παρουσιάζουμε τη βασική θεωρία της στρατηγικής συμπεριφοράς των πελατών σε Ουρές Αναμονής. Στο δεύτερο μέρος, παρουσιάζουμε δυο εργασίες με δομή καθυστερημένης πληροφορίας και με ποιο τρόπο αυτή επηρεάζει τη στρατηγική συμπεριφορά των πελατών. Στο τρίτο μέρος της εργασίας παρουσιάζομαι ένα πρωτότυπο μοντέλο με δομή καθυστερημένης πληροφορίας και προσπαθούμε να εξετάσουμε πως επηρεάζεται η στρατηγική συμπεριφορά των πελατών.In many applications customers arrive in a service system and decide whether to join it or not, without knowing the number of customers in the system. Later, the joining customers get informed about their position in the system and then they can decide wheter to stay in it or balk. The main question that arises from this description, is in what way this delayed information influence strategic customer behavior. In the first part of this MSc Thesis we present the main theory of Strategic Customers in Queueing Systems. In the second part, we present two papers with a dealyed information structure. In the third part, we present a new model with a delayed information structure and we try to analyze in what way this dealyed information influence strategic customer behavior

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"