A model for special-service circuit activity

Abstract

We describe a model for special-service circuit activity to assist in forecasting, provisioning, and “churn” studies. We assume that customers order a random number of circuits for an exponentially distributed period of time and that the rate of new connect orders grows exponentially with time. These assumptions yield simple formulae giving the means and variances of the number of active circuits at a future time and the total number of connected and disconnected circuits during a future period. Distributions of these variables can, in principle, also be computed. There are three important parameters characterizing the model: growth rate, disconnect rate, and batchiness; we describe their physical meaning and discuss methods to estimate them. This document describes the analytical portion of an effort to develop a model based on the physics of special-service circuit activity.