Multifactor Poisson and Gamma-Poisson Models for Call Center Arrival Times

It is usually assumed that the arrivals to a queue will follow a Poisson process. In its simplest form, such a process has a constant arrival rate. However this assumption is not always valid in practice. We develop statistical procedures to test a stochastic process is an inhomogeneous Poisson process, and show that call arrivals to a real-life call center follow such a Poisson process with an inhomogeneous arrival rate over time. We find that the inhomogeneous Poisson assumption is reasonably well satisfied. Then we derive statistical models that can be used to construct predictions of the inhomogeneous arrival rate, and provide estimates of the parameters in the models. The conclusion that the process is well modelled as an inhomogeneous Poisson process, together with a statistical model for the arrival rate in that process, could be used to enable realistic calculations or simulations of the performance of the queuing system. The models can also be used to predict future call volumes or workloads to the system.