Poisson Mixtures for Call Centre Arrival Rate Quantile Forecasting

Thursday 19 April 2012
11:00 am - 12:00 pm
Event type Seminar
Location John Crank Room 128
Speaker: James Taylor Oxford University

Abstract

Efficient call center staffing relies on forecasts for the call arrival rate. The uncertainty in arrival rates has prompted call volumes to be modeled using a Poisson mixture with a convenient distributional assumption for the rate. For example, assuming a gamma distributed arrival rate implies a negative binomial distribution for the counts. As an alternative to this fully parametric approach, we present a Poisson mixture model that directly estimates individual quantiles of the rate distribution. The literature has highlighted the link between quantile regression and quasi-maximum likelihood based on an asymmetric Laplace distribution. Our proposal is to model the call volumes as Poisson with an asymmetric Laplace mixing (PALM) distribution. We also consider a Poisson distribution with alternative tick exponential mixing (PATEM). The models are fitted using quasi-maximum likelihood to deliver quantile estimates of the rate. These estimates can be used to construct a density forecast, or plugged into the Erlang formula to give a stochastic guarantee for the service level. We evaluate the models using simulated data, and illustrate their implementation for real call center arrivals data.

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