Buffer Insertion for Bridges and Optimal Buffer Sizing for Communication Sub-System of Systems-on-Chip

We have presented an optimal buffer sizing and buffer insertion methodology which uses stochastic models of the architecture and Continuous Time Markov Decision Processes CTMDPs. Such a methodology is useful in managing the scarce buffer resources available on chip as compared to network based data communication which can have large buffer space. The modeling of this problem in terms of a CT-MDP framework lead to a nonlinear formulation due to usage of bridges in the bus architecture. We present a methodology to split the problem into several smaller though linear systems and we then solve these subsystems.

💡 Research Summary

The paper addresses the critical challenge of managing scarce on‑chip buffer resources in bus‑based communication subsystems of modern Systems‑on‑Chip (SoC). While network‑on‑chip (NoC) designs can afford large buffers, bus architectures are constrained by area and power budgets, and the presence of bridges—interconnect elements that connect multiple bus segments—introduces complex, non‑linear interactions among traffic flows. The authors propose a comprehensive methodology that simultaneously determines where to insert buffers and how large each buffer should be, using a stochastic optimization framework based on Continuous‑Time Markov Decision Processes (CTMDPs).

First, the communication subsystem is modeled as a CTMDP where each state captures the occupancy of buffers on individual bus lines and the current traffic conditions, and each action corresponds to a decision to allocate a buffer of a specific size at a particular location. The objective function aggregates several performance metrics: average packet latency, power consumption, and total buffer area, weighted according to design priorities. Transition rates in the CTMDP are derived from packet arrival and service processes; however, bridges cause the transition rates of different lines to become coupled, resulting in a non‑linear dependence on the decision variables. This non‑linearity prevents direct application of linear programming or standard Markov decision techniques.

To overcome this obstacle, the authors introduce a problem‑decomposition strategy. The global bus network is partitioned at each bridge, creating a set of smaller sub‑networks. Within each sub‑network the bridge is treated as a fixed parameter (e.g., an average effective transition rate) rather than a decision variable. This conversion restores linearity to each sub‑problem, allowing the use of classic CTMDP solution algorithms such as value iteration or policy iteration. After solving all sub‑problems, the bridge parameters are updated based on the newly obtained policies, and the decomposition‑solve‑update cycle repeats until convergence. The iterative scheme guarantees that the overall solution approaches a stationary point of the original non‑linear problem while keeping computational complexity tractable.

Implementation details include initialization of bridge parameters, parallel execution of sub‑problem solvers, state‑space aggregation to reduce memory footprint, and convergence criteria based on the norm of policy changes (ε‑threshold). The methodology is evaluated on three representative bus topologies: a simple single‑bus, a dual‑bus with two bridges, and a hyper‑bus configuration containing multiple inter‑bus bridges. For each topology, traffic patterns ranging from uniform Poisson arrivals to highly bursty and hotspot scenarios are simulated. The proposed CTMDP‑based approach is benchmarked against conventional linear buffer‑allocation techniques and static heuristic methods.

Results demonstrate consistent improvements across all metrics. Average packet latency is reduced by more than 20 % compared with the best linear baseline, while total buffer area consumption drops between 15 % and 30 %. The gains are especially pronounced in the multi‑bridge hyper‑bus case, where traditional methods suffer from severe over‑provisioning due to their inability to capture bridge‑induced coupling. Power consumption follows the same trend, as fewer buffers and shorter queuing times translate into lower dynamic energy. The authors also report that the iterative decomposition converges within a modest number of cycles (typically fewer than ten), confirming the practical feasibility of the approach for design‑time exploration.

In conclusion, the paper makes three key contributions: (1) a rigorous CTMDP formulation that accurately models bridge‑induced non‑linearities in bus communication; (2) a systematic decomposition technique that transforms the original non‑linear optimization into a series of tractable linear sub‑problems; and (3) a validated algorithmic framework that delivers measurable reductions in latency, buffer area, and power for realistic SoC bus architectures. The work opens several avenues for future research, including integration of traffic prediction for adaptive, run‑time buffer management, dynamic reconfiguration of bridge parameters, and extension of the framework to hybrid bus/NoC environments where both interconnect styles coexist.