The impact of retrials on call center performance

Abstract

This paper models a call center as a Markovian queue with multiple servers, where customer balking, impatience, and retrials are modeled explicitly. The resulting queue is analyzed both in a stationary and non-stationary setting. For the stationary setting a fluid approximation is proposed, which overcomes the computational burden of the continuous time markov chain analysis, and which is shown to provide an accurate representation of the system for large call centers with high system load. An insensitivity property of the retrial rate to key system parameters is established. The fluid approximation is shown to work equally well for the nonstationary setting with time varying arrival rates. Using the fluid approximation, the paper explores the retrial phenomenon for a real call center. The model is used to estimate the real arrival rates based on demand data where retrials cannot be distinguished from first time calls. This is a common problem encountered in call centers. Through numerical examples, it is shown that disregarding the retrial phenomenon in call centers can lead to huge distortions in subsequent forecasting and staffing analysis.

The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research

“…This type of retrial behavior and its influence on performance is modeled by Mandelbaum et al (1999) and Aguir et al (2004). Approximations, in particular a fluid approximation, perform very well for such systems.…”

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

“…An adjusted fluid approximation for this system is proposed by Ko and Gautam [127]. Aguir et al [4] modify the queueing model and include the effect of balking but assume a time-invariant service rate. By choosing a balking probability of 0 if L S o K and 1 otherwise, their model can also approximate systems with a finite waiting room.…”

“…Whereas Sze [207], Aguir et al [4], and Ridley et al [192] describe the performance evaluation of call centers, all other references cited in this paragraph concentrate on the development of staffing algorithms for call centers. Kolesar and Green [129] focus on the analysis of the peak hour in their staffing analysis.…”

“…Abandonments are considered by Feldman et al [69], Hampshire et al [95], Bertsimas and Doan [17], Dietz [60], and Kim and Ha [118]. Customers who reenter the system after abandonment (retrials) are analyzed by Sze [207] and Aguir et al [4]. Sze [207] considers abandonments as part of the arriving jobs that require a service time of zero.…”

Service Engineering in Action: The Palm/Erlang-A Queue, with Applications to Call Centers

“…In addition, we assume out retrials and return calls, which corresponds to absorbing them within the arrivals. (See, for example, Aguir et al [2] for an analysis that takes retrials into account.) However, and unlike most models used in practice, here we do acknowledge and accommodate abandonment.…”