Maximizing quality of aggregation (QoA) is an essential requirement for real-time wireless sensor networks (WSNs) where the participation of all sensor nodes in data aggregation is hampered by the underlying sink deadline and interference constraints. This problem, however, remains unsolved under the physical interference model that captures the reality more accurately than the widely used graph-based models. In this paper, we formulate an optimization problem of maximizing QoA under deadline and interference constraints in commonly seen tree-based WSNs. We prove the problem to be NP-complete, and then propose a suboptimal scheduling algorithm which relies on a Markov approximation framework and modifies the matching graphs in order to handle the globally-imposed interference constraints. The problem and its solution are then coupled with successive interference cancellation (SIC) to improve QoA by increasing the number of concurrent transmissions. Our evaluation has shown the proposed solution to be effective under the physical interference model, both with and without SIC.