Future long-pulse magnetic confinement fusion reactors will require density and isotopic mixture control using steady-state repeating pellet injectors. For high-energy density burning plasmas, pellet velocities of 1 km/s and above will be required for sufficient plasma penetration to achieve high fueling efficiency. Currently, steady-state repeating injection systems utilize cryogenic extruder systems to produce an extrusion of solid deuterium or deuterium-tritium. In repeating light gas gun injectors, the solid extrusion is cut and simultaneously loaded into a barrel. Once loaded, a fast operating gas valve delivers a high pressure burst of gas to accelerate the pellet down the barrel and into the machine. This process takes ~10 ms to achieve. Adequate gas pumping of the extruder exhaust and injection line propellant gas collection chambers is necessary for optimal operation of the pellet fueling system. Excess solid from the extruder sublimates in an exhaust chamber. The gas pressure in the extruder exhaust chamber must remain low to maintain low heating loads on the cooling mechanism (cryorefrigerators or liquid helium flow) and to reduce thermal conduction to the extrusion. Pumping the injection line chambers is necessary to limit propellant gas flow into the machine. A numerical simulation code was created to predict temporal pumping performance for these repeating pellet injection systems. This paper outlines the methods and assumptions used to create this model and compares results to the pellet injection system currently employed on DIII-D, the steady-state pellet injection system planned for the Wendelstein 7-X, and a brief analysis of the ITER conceptual pellet fueling system.