A robust sequential projection algorithm for traffic load forecasting

Forecasts of busy season trunk group traffic loads are required for planning the Bell System's message network. Forecasting algorithms currently in use obtain estimates of future loads by multiplying the most recent measurement of busy season load by an aggregate growth factor. Because of statistical errors in measured loads and differences between individual trunk group and aggregate growth factors, the resulting forecasts can have large statistical errors. In this paper we extend earlier work to develop a new algorithm, called the sequential protection algorithm (SPA), based on a linear two-state Kalman filter, together with logic for detecting and responding to unusually large measurement errors or changes in trend. In typical applications of Kalman filtering, the statistics of system noises, measurement errors, and initial conditions are known and the filter parameters (Kalman gains) are selected accordingly. For our application, however, these statistics cannot be determined without error. Consequently, we develop a method for selecting robust filter parameters which provide improved performance, independent of system noises, measurement errors, and initial conditions. In particular, under the assumption of linear growth for 5-year intervals, the average rms 1-year forecast error of SPA is about 10 percent less than that of the existing algorithms. Field test results confirm the theoretical results presented here. Accordingly, specifications have been written for inclusion of SPA in the Bell System's standard trunk forecasting systems.