Quantitative Verification of Scheduling Heuristics

Computer systems use many scheduling heuristics to allocate resources. Understanding their performance properties is hard because it requires a representative workload and extensive code instrumentation. As a result, widely deployed schedulers can make poor decisions leading to unpredictable performance. We propose a methodology to study their specification using automated verification tools to search for performance issues over a large set of workloads, system characteristics and implementation details. Our key insight is that much of the complexity of the system can be overapproximated without oversimplification, allowing system and heuristic developers to quickly and confidently characterize the performance of their designs. We showcase the power of our methodology through four case studies. First, we produce bounds on the performance of two classical algorithms, SRPT scheduling and work stealing, under practical assumptions. Then, we create a model that identifies two bugs in the Linux CFS scheduler. Finally, we verify a recently made observation that TCP unfairness can cause some ML training workloads to spontaneously converge to a state of high network utilization.