Probabilistic Verification for Reliability of a Two-by-Two Network-on-Chip System

Abstract

Modern network-on-chip (NoC) systems face reliability issues due to process and environmental variations. The power supply noise (PSN) in the power delivery network of a NoC plays a key role in determining reliability. PSN leads to voltage droop, which can cause timing errors in the NoC. This paper makes a novel contribution towards formally analyzing PSN in NoC systems. We present a probabilistic model checking approach to analyze key features of PSN at the behavioral level in a 2 × 2 mesh NoC with a uniform random traffic load. To tackle state explosion, we apply incremental abstraction techniques, including a novel probabilistic choice abstraction, based on observations of NoC behavior. The Modest Toolset is used for probabilistic modeling and verification. Results are obtained for several flit injection patterns to reveal their impacts on PSN. Our analysis finds an optimal flit pattern generation with zero probability of PSN events and suggests spreading flits rather than releasing them in consecutive cycles in order to minimize PSN.

An Overview of Modest Models and Tools for Real Stochastic Timed Systems

“…Figure 2: Architecture of the 2 × 2 NoC [44] To study PSN in NoC architectures, we modelled in Modest and analysed with mcsta first a single central router of a NoC [42] and later a two-by-two NoC consisting of four symmetric routers [44] as shown in Figure 2. We focus on the latter in this section.…”

“…Figure 3: CDF for inductive noise events [44] The resulting model could be model-checked for up to 30 clock cycles with every-other-cycle flit generation by unfolding the clock cycle counter into the state space, and up to any number of clock cycles by using the unfolding-free modified iteration technique of [27], in essence computing the entire cumulative distribution function (CDF) as shown in Figure 3. This is due to an interesting effect of the different flit generation patterns: With every-other-cycle generation, the buffers slowly fill up with flits to various destinations; the full state space that includes all combinations of buffer occupancies with different flits is too large to handle today.…”

“…Similarly, our attempts to use Storm's binary decision diagram-based state space exploration did not provide scalability improvements, possibly due to the model not being as structured as we think it is, or simply due to a bad variable ordering in the model. For further details on this first case study, we refer the interested reader to the original paper that was presented at FMICS 2021[44].…”

“…Acknowledgments. I thank my co-authors for the papers underlying the three case studies [16,32,42,44], without whom my presentation at MARS and this summary paper would not have been possible: Prabal Basu, Koushik Chakraborty, Pedro R. D'Argenio, Juan A. Fraire, Holger Hermanns, Rajesh Jayashankara Shridevi, Benjamin Lewis, Riley Roberts, Sanghamitra Roy, and Zhen Zhang.…”