Continuous Fluid Modeling of Credit-Based Flow Control for HPC Interconnection Networks

Most modern HPC interconnects rely on the lossless properties of credit-based flow control for achieving high throughput and low latency transfers. However, this flow control method produces complex transient dynamics, throughput oscillations driven by delayed credit feedback, backpressure propagation, and head-of-line blocking. While packet-level discrete-event simulators can faithfully reproduce these behaviors, they have scaling limitations due to their high computation costs. This paper proposes a more scalable fluid model for capturing the behaviors by formulating these dynamics as a coupled system of delay differential equations governing backlog accumulation, credit depletion, and proportional bandwidth sharing, integrated via a fourth-order Runge–Kutta method with history interpolation. The model first characterizes transient phase evolution at a single contention point, then generalizes to multi-router topologies where per-hop credit pools and heterogeneous propagation delays introduce cross-hop coupling and head-of-line blocking through shared output buffers. Compared against the CODES packet-level simulator, the fluid model closely reproduces transient throughput for both single-hop and multi-hop configurations while achieving 22–98×× speedup.