Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models

Abstract

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.

The impact of special days in call arrivals forecasting: A neural network approach to modelling special days

“…Developments in time series forecasting for call centre arrival data have focused primarily on advanced methods for capturing the complex seasonal patterns in the data as well as dealing with the high-frequency, big data aspects of the problem (for examples see Antipov and Meade, 2002;Shen and Huang, 2005;Taylor, 2008a;Shen, 2009;Aldor-Noiman et al, 2009;Taylor and Snyder, 2012;Ibrahim and L'Ecuyer, 2013). Meanwhile, simple methods such as the intraweek seasonal moving average, have been shown to outperform more advanced ones (Tandberg et al, 1995;Taylor, 2010b;Ibrahim and L'Ecuyer, 2013), with Taylor (2008a) suggesting "to use more advanced methods may not be the solution".…”

“…Meanwhile, simple methods such as the intraweek seasonal moving average, have been shown to outperform more advanced ones (Tandberg et al, 1995;Taylor, 2010b;Ibrahim and L'Ecuyer, 2013), with Taylor (2008a) suggesting "to use more advanced methods may not be the solution". On the other hand flexible methods, such as neural networks, have been overlooked, which we attempt to address here.…”

“…Note that we restrict our attention to time series methods that forecast call arrivals volume and we do not investigate models for call arrivals rate, for example by consider other classes of methods e.g. those which incorporate stochastic models (Avramidis et al, 2004) and those based on assumptions of a Poisson process (Aldor-Noiman et al, 2009;Ibrahim and L'Ecuyer, 2013).…”

On the modeling and forecasting of call center arrivals

“…Again, the dependence here can be modeled via a copula, after fitting the marginals individually. The simplest and more practical type of copula for this is probably the normal copula, used for example by Kim, Kenkel, and Brorsen (2012) and Ibrahim and L'Ecuyer (2012). However, empirical data suggests that for certain pairs of call types, the coefficient of upper or lower tail dependence, which measures the strength of the dependence in the right or left tail of the distribution, is quite different from that implied by a normal copula.…”

“…This agrees with (P3) and (P4). We applied the square-root transformation Y i, j = X i, j + 1/4 to our data, and then adjusted the FE and ME models described in Section 4, without special days; see Ibrahim and L'Ecuyer (2012) for more details. We also considered the Holt-Winters (HW) smoothing method, with a daily seasonality.…”