We present an analytical model for an autonomous vehicle storage and retrieval system (AVS/RS). The system is modeled as a semi-open queueing network (SOQN). An SOQN consists of customers, a secondary resource and servers. Each arriving customer is paired with the secondary resource. The two visit the set of servers required by the customer in the specified sequence. In the context of an AVS/RS, storage/retrieval (S/R) transactions are customers and the autonomous vehicles are the secondary resources. If an S/R transaction requires a vertical movement, it uses a lift. The lifts and horizontal travel times to and from a storage space are modeled as servers. First, we define all possible scenarios for storage and retrieval transactions and their occurrence probabilities. Second, we derive general travel times of vehicles and lifts by considering all possible locations of the two devices based on the predefined storage and retrieval scenarios, defined in step 1. Third, each scenario is modeled as a customer type and these customer classes are aggregated into a single class. Thus, we model the system as a single-class, multiple-server, SOQN. Finally , we solve the SOQN using an approximate method and obtain the performance measures. We apply the method to analyze a warehouse in France that utilizes AVS/RS.