[en] A model for calculating the integrated luminosity of beams stored in the Tevatron collider will be presented. The model determines the instantaneous luminosity by calculating the overlap integral of bunched beams passing through the interaction region. The calculation accounts for the variation in beam size due to the beta functions and also for effects due to finite longitudinal emittance and non-zero dispersion in the interaction region. The integrated luminosity is calculated for the beams as they evolve due to processes including collisions and intrabeam scattering. The model has been applied to both the extant and upgraded Tevatron collider, but is not limited to them. The original motivation for developing the computer model was to determine the reduction in luminosity due to beams with non-zero longitudinal emittances. There are two effects: the transverse beam size is increased where the dispersion is non-zero; the finite length of the beam bunch combined with an increasing β function results in an increased transverse beam size at the ends of the bunch. The derivation of a sufficiently useful analytic expression for the luminosity proved to be intractable. Instead, a numerical integration computer program was developed to calculate the luminosity in the presence of a finite longitudinal emittance. The program was then expanded into a model which allows the luminosity to vary due to changes in emittances and reduction in bunch intensities. At that point, it was not difficult to calculate the integrated luminosity. 5 refs., 2 figs., 4 tabs