We demonstrate that autonomous-assisted delivery can yield significant improvements relative to today's system in which a delivery person must park the vehicle before delivering packages. We model an autonomous vehicle that can drop off the delivery person at selected points in the city where the delivery person makes deliveries to the final addresses on foot. Then, the vehicle picks up the delivery person and travels to the next reloading point. In this way, the delivery person would never need to look for parking or walk back to a parking place. Based on the number of customers, driving speed of the vehicle, walking speed of the delivery person, and the time for loading packages, we characterize the optimal solution to the autonomous case on a solid rectangular grid of customers, showing the optimal solution can be found in polynomial time. To benchmark the completion time of the autonomous case, we introduce a traditional model for package delivery services that includes the time to search for parking. If the time to find parking is ignored, we show the introduction of an autonomous vehicle reduces the completion time of delivery to all customers by 0%-33%. When nonzero times to find parking are considered, the delivery person saves 30%-77% with higher values achieved for longer parking times, smaller capacities, and lower fixed time for loading packages.