On the modeling and forecasting of call center arrivals

Abstract

We review and discuss the key issues in building statistical models for the call arrival process in telephone call centers, and then we survey and compare various types of models proposed so far. These models are used both for simulation and to forecast incoming call volumes to make staffing decisions and build (or update) work schedules for agents who answer those calls. Commercial software and call center managers usually base their decisions solely on point forecasts, given in the form of mathematical expectations (conditional on current information), but distributional forecasts, which come in the form of (conditional) probability distributions, are generally more useful, in particular in the context of simulation. Building realistic models is not simple, because arrival rates are themselves stochastic, time-dependent, dependent across time periods and across call types, and are often affected by external events. As an illustration, we evaluate the forecasting accuracy of selected models in an empirical study with real-life call center data.

Modelling for the proposed roll-out of the ‘111’ service in Wales: a case study

“…In this case study, we consider both multiple queues associated with the different level of priorities attached to the incoming calls from both NHS DW and GPOoH and a multi-skill workforce answering the two sets of calls. Ibrahim et al [15] highlight that stochastic simulation provides a more realistic evaluation tool when applied to multi-skill centres as in our case study where we have five different staff types: GPs, nurse advisors, health information advisors, call handlers and dental nurses.…”

Rate-Based Daily Arrival Process Models with Application to Call Centers

“…Our second data set is from the call center of a major Canadian company, and is taken from Ibrahim et al (2012) and Ibrahim and L'Ecuyer (2013). The center operates from 8 a.m. to 7 p.m.…”

“…Shen (2010) and Ibrahim et al (2015b) give overviews of existing models, which typically have a regression or time series flavor. For example, Weinberg et al (2007) used a Bayesian approach to sample from the forecast distributions based on a linear regression data model, while Ibrahim et al (2012), Aldor-Noiman et al (2009), Brown et al (2005 used different variants of linear regression models to produce point forecasts of daily call volumes.…”

“…This is consistent with the assumption that arrivals are from a Poisson process with unknown (perhaps random) constant rate over the period. But this is much less convenient and efficient than generating the arrivals one by one directly from the constant rate when this rate is known (Ibrahim et al 2012). …”

Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers

“…Among important sources of uncertainty are call arrival rates which are typically both time-varying and stochastic, service times which are random and whose distribution may depend on the call type and the agent who handles it, and agents who may not show up or may not follow their planned schedules; see Bhulai and Koole (2003), Avramidis et al (2004), Avramidis and L'Ecuyer (2005), Aldor-Noiman et al (2009), Gans et al (2010), Ibrahim et al (2012), Oreshkin et al (2015), and references therein.…”