A logical model of multi-tiered persistent storage provides a view of data where all available storage resources are distributed over a number of levels depending on the data transfer parameters and capacities. The efficient parallelization of data transfers in multi-tiered persistent storage is a significant challenge for a pipelined data processing model. This work examines a category of database applications implemented as sequences of operations that transfer data between the levels of multi-tiered persistent storage. The concept of EPN: Extended Petri Nets represents how database applications can be processed in parallel. A proposed transformation involves converting EPN into sequences of parallel data transfers. Additionally, a method is demonstrated for partitioning these sequences of data transfers, with the goal of reducing the total number of conflicts when data transfers occur between the levels of multi-tiered persistent storage. The paper proposes new rule-based algorithms for scheduling parallel data transfers that minimize total data transfer time. The objectives of the new algorithms are to evenly distribute the workload among the data transfer processes and reduce their idle time. Several experiments have confirmed the effectiveness of the new algorithms in generating parallel data transfer plans.