A question that database administrators (DBAs) routinely need to answer is how long a batch query workload will take to complete. This question arises, for example, while planning the execution of different report-generation workloads to fit within available time windows. To answer this question accurately, we need to take into account that the typical workload in a database system consists of mixes of concurrent queries. Interactions among different queries in these mixes need to be modeled, rather than the conventional approach of considering each query separately. This paper presents a new approach for estimating workload completion times that takes the significant impact of query interactions into account. This approach builds performance models using an experiment-driven technique, by sampling the space of possible query mixes and fitting statistical models to the observed performance at these samples. No prior assumptions are made about the internal workings of the database system or the cause of query interactions, making the models robust and portable. We show that a careful choice of sampling and statistical modeling strategies can result in accurate models, and we present a novel interaction-aware workload simulator that uses these models to estimate workload completion times. An experimental evaluation with complex TPC-H queries on IBM DB2 shows that this approach consistently predicts workload completion times with less than 20% error.