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Temporal isolation is one of the most significant challenges that must be addressed before Multi-Processor Systems-on-Chip (MPSoCs) can be widely adopted in mixed-criticality systems with both time-sensitive real-time (RT) applications and performance-oriented non-real-time (NRT) applications. Specifically, the main memory subsystem is one of the most prevalent causes of interference, performance degradation and loss of isolation. Existing memory bandwidth regulation mechanisms use static, dynamic, or predictive DRAM bandwidth management techniques to restore the execution time of an application under contention as close as possible to the execution time in isolation. In this paper, we propose a novel distribution-driven regulation whose goal is to achieve a timeliness objective formulated as a constraint on the probability of meeting a certain target execution time for the RT applications. Using existing interconnect-level Performance Monitoring Units (PMU), we can observe the Cumulative Distribution Function (CDF) of the per-request memory latency. Regulation is then triggered to enforce first-order stochastical dominance with respect to a desired reference. Consequently, it is possible to enforce that the overall observed execution time random variable is dominated by the reference execution time. The mechanism requires no prior information of the contending application and treats the DRAM subsystem as a black box. We provide a full-stack implementation of our mechanism on a Commercial Off-The-Shelf (COTS) platform (Xilinx Ultrascale+ MPSoC), evaluate it using real and synthetic benchmarks, experimentally validate that the timeliness objectives are met for the RT applications, and demonstrate that it is able to provide 2.2x more overall throughput for NRT applications compared to DRAM bandwidth management-based regulation approaches.