We consider different statistical models for the call arrival process in telephone call centers. We evaluate the forecasting accuracy of those models by describing results from an empirical study analyzing real-life call center data. We test forecasting accuracy using different lead times, ranging from weeks to hours in advance, to mimic real-life challenges faced by call center managers. The models considered are: (i) a benchmark fixed-effects model which does not exploit any dependence structures in the data; (ii) a mixed-effects model which takes into account both interday (day-to-day) and intraday (within day) correlations; (iii) two new bivariate mixed-effects models, for the joint distribution of the arrival counts to two separate queues, which exploit correlations between different call types. Our study shows the importance of accounting for different correlation structures in the data.

Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative real-time delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delay-history estimators to the standard estimator based on the queue length (QL), commonly used in practice, which requires knowledge of the mean interval between successive service completions in addition to the QL. We characterize performance by the mean squared error (MSE). We do an analysis and conduct simulations for the standard GI/M/s multiserver queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the many-server and classical heavy-traffic (HT) limiting regimes.delay estimation, real-time delay estimation, delay prediction, delay announcements, many-server queues, call centers, heavy traffic

The effective management of call centers is a challenging task mainly because managers are consistently facing considerable uncertainty. Among important sources of uncertainty are call arrival rates which are typically time-varying, stochastic, dependent across time periods and across call types, and often affected by external events. Accurately modeling and forecasting future call arrival volumes is a complicated issue which is critical for making important operational decisions, such as staffing and scheduling, in the call center. In this paper, we review the existing literature on modeling and forecasting call arrivals. We also discuss the key issues in building good statistical arrival models. Additionally, we evaluate the forecasting accuracy of selected models in an empirical study with real-life call center data. We conclude by summarizing future research directions in this important field.

We use heavy-traffic limits and computer simulation to study the performance of alternative real-time delay estimators in the overloaded GI/GI/s+GI multiserver queueing model, allowing customer abandonment. These delay estimates may be used to make delay announcements in call centers and related service systems. We characterize performance by the expected mean squared error in steady state. We exploit established approximations for performance measures with a nonexponential abandonment-time distribution to obtain new delay estimators that effectively cope with nonexponential abandonment-time distributions.delay estimation, delay announcements, call centers, many-server queues, customer abandonment, simulation, heavy traffic

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work.