Modeling Daily Arrivals to a Telephone Call Center

Abstract

We develop stochastic models of time-dependent arrivals, with focus on the application to call centers. Our models reproduce three essential features of call center arrivals observed in recent empirical studies: a variance larger than the mean for the number of arrivals in any given time interval, a time-varying arrival intensity over the course of a day, and nonzero correlation between the arrival counts in different periods within the same day. For each of the new models, we characterize the joint distribution of the vector of arrival counts, with particular focus on characterizing how the new models are more flexible than standard or previously proposed models. We report empirical results from a study on arrival data from a real-life call center, including the essential features of the arrival process, the goodness of fit of the estimated models, and the sensitivity of various simulated performance measures of the call center to the choice of arrival process model.

Interday Forecasting and Intraday Updating of Call Center Arrivals

“…For example, it is typical that there is a peak around 11:00AM followed by a second, lower peak around 2:00PM. As an illustration, Figure 1 Our data appear to possess heteroscedasticity (i.e., nonconstant variance) and overdispersion (i.e., variance greater than mean) (Avramidis et al 2004), as shown in Figure 1(c).…”

“…There are empirical justifications for the within-day updating, as both Avramidis et al (2004) and Steckley et al (2004) report evidence of positive correlation among time periods within a given day, i.e. intraday dependence.…”

“…Recently, with the availability of call-by-call data, stochastic models of call arrivals that take into account the intraday dependence have been introduced. Avramidis et al (2004) develop doubly stochastic models that reproduce three empirically observed features of call arrival data, overdispersion, time-varying rate and intraday dependence. Brown et al (2005) consider a time-varying Poisson process with random rate, and suggest a multiplicative two-way mixed-effects model to forecast future rate.…”

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

“…Avramidis et al (2004) proposed several stochastic models including a doubly stochastic Poisson arrival process with a random arrival rate. Their models reproduce essential characteristics of call center arrivals, such as: (i) a variance considerably higher than with Poisson arrivals, as observed by Jongbloed and Koole (2001), and (ii) strong intraday correlations, as in Tanir and Booth (2001).…”

“…If a distributional forecast is available for the arrival rate, then we can simulate by first generating the rate, then the arrivals from a Poisson process with that same rate. Alternatively, if a distributional forecast in available only for the counts, we can generate the arrival counts in each period (from their joint distribution), then spread the arrivals of each period uniformly and independently in that period (this is correct if we assume that the arrival rate is constant in each period), e.g., see Avramidis et al (2004).…”