On the influence of production on utilization functions - obsolescence or increased use

Abstract

We study the influence of production on utilization functions. A concrete example of this is the influence of the growth of literature on the obsolescence (aging) of this literature. Here, synchronous as well as diachronous obsolescence is studied. Assuming an increasing exponential function for production and a decreasing one for aging, we show that, in the synchronous case, the larger the increase in production, the larger the obsolescence. In the diachronous case the opposite relation holds: the larger the increase in production the smaller the obsolescence rate. This has also been shown previously by Egghe but the present proof is shorter and yields more insight in the derived results. If a decreasing exponential function is used to model production the opposite results are obtained. It is typical for this study that there are two different time periods: the period of production (growth) and - per year appearing in the production period - the period of aging (measured synchronously and diachronously). The interaction of these periods is described via convolutions (discrete as well as continuous).