We estimate the potential for a dynamically managed parking reservation system to increase the accommodation of real-time delivery demand by implementing a sliding time window mixed integer linear programming parking slot assignment formulation. Through our research, we reveal key trade-offs in the performance of a dynamic reservation system based on the lead time of a parking request from submission to requested arrival time, flexibility in the requested arrival time, and arrival time uncertainty. Comparing results across a range of scenarios, we find that a reservation system in our representative case can either increase parking accommodation by up to 330 h per space per year or reduce parking accommodation by up to 130 h per space per year, relative to first-come first-serve. Reservation systems tend to increase parking accommodation most when drivers have flexible but reliable arrival times, requests are made in advance, and demand is low or moderate. Reservation systems can especially reduce parking accommodation when unoccupied buffer periods between reservations are used to guarantee reservations due to uncertainty in arrival and departure times. Our results suggest that the application of dynamic curb reservation systems may be most appropriate for targeted applications where drivers have flexible but reliable arrival times.