Modeling and Verification of Dynamic Command Scheduling for Real-Time Memory Controllers

In modern multi-core systems with multiple real-time (RT) applications, memory traffic accessing the shared SDRAM is increasingly diverse, e.g., transactions have variable sizes. RT memory controllers with dynamic command scheduling can efficiently address the diversity by issuing appropriate commands subject to the SDRAM timing constraints. However, the scheduling dependencies between commands make it challenging to derive tight bounds for the worst-case response time (WCRT) and the worst-case bandwidth (WCBW) of a memory controller. Existing modeling and analysis techniques either do not provide tight WCRT and WCBW bounds for diverse memory traffic with variable transaction sizes or are difficult to adapt to different RT memory controllers. This paper models a memory controller using Timed Automata (TA), where model checking is applied for analysis. Our TA model is modular and accurately captures the behavior of a RT memory controller with dynamic command scheduling. We obtain WCRT and WCBW bounds, which are validated by simulating the worst- case transaction traces obtained by model checking with a cycle-accurate model of the memory controller. Our method outperforms three state-of-the-art analysis techniques. We reduce WCRT bound by up to 20%, while the average improvement is 7.7%, and increase the WCBW bound by up to 25% with an average improvement of 13.6%. In addition, our modeling is generic enough to extend to memory controllers with different mechanisms.