Extreme Volume Detection for Managed Print Services

A managed print service (MPS) manages the printing, scanning and facsimile devices in an enterprise to control cost and improve availability. Services include supplies replenishment, maintenance, repair, and use reporting. Customers are billed per page printed. Data are collected from a network of devices to facilitate management. The number of pages printed per device must be accurately counted to fairly bill the customer. Software errors, hardware changes, repairs, and human error all contribute to “meter reads” that are exceptionally high and are apt to be challenged by the customer were they to be billed. Account managers periodically review data for each device in an account. This process is tedious and time consuming and an automated solution is desired. Exceptional print volumes are not always salient and detecting them statistically is prone to errors owing to nonstationarity of the data. Mean levels and variances change over time and usage is highly auto correlated which precludes simple detection methods based on deviations from an average background. A solution must also be computationally inexpensive and require little auxiliary storage because hundreds of thousands of streams of device data must be processed. We present an algorithm and system for online detection of extreme print volumes that uses dynamic linear models (DLM) with variance learning. A DLM is a state space time series model comprising a random mean level system process and a random observation process. Both components are updated using Bayesian statistics. After each update, a forecasted value and its estimated variance are calculated. A read is flagged as exceptionally high if its value is highly unlikely with respect to a forecasted value and its standard deviation. We provide implementation details and results of a field test in which error rate was decreased from 26.4% to 0.5% on 728 observed meter reads.