Phase-Scheduled Multi-Agent Systems for Token-Efficient Coordination

Abstract: Multi-agent systems (MAS) powered by LLMs suffer from severe token inefficiency arising from two compounding sources: (i) unstructured parallel execution, where all agents activate simultaneously irrespective of input readiness; and (ii) unrestricted context sharing, where every agent receives the full accumulated context regardless of relevance. Existing mitigation strategies - static pruning, hierarchical decomposition, and learned routing - treat coordination as a structural allocation problem and fundamentally ignore its temporal dimension. We propose Phase-Scheduled Multi-Agent Systems (PSMAS), a framework that reconceptualizes agent activation as continuous control over a shared attention space modeled on a circular manifold. Each agent i is assigned a fixed angular phase theta_i in the range [0, 2*pi], derived from the task dependency topology; a global sweep signal phi(t) rotates at velocity omega, activating only agents within an angular window epsilon. Idle agents receive compressed context summaries, reducing per-step token consumption. We implement PSMAS on LangGraph, evaluate on four structured benchmarks (HotPotQA-MAS, HumanEval-MAS, ALFWorld-Multi, WebArena-Coord) and two unstructured conversational settings, and prove stability, convergence, and optimality results for the sweep dynamics. PSMAS achieves a mean token reduction of 27.3 percent (range 21.4-34.8 percent) while maintaining task performance within 2.1 percentage points of a fully activated baseline (p < 0.01, n = 500 per configuration), and outperforms the strongest learned routing baseline by 5.6 percentage points in token reduction with 2.0 percentage points less performance drop. Crucially, we show that scheduling and compression are independent sources of gain: scheduling alone accounts for 18-20 percentage points of reduction, robust to compression degradation up to alpha = 0.40.

• The paper presents PSMAS, a continuous control framework that schedules agent activations on a circular manifold to significantly reduce redundant token usage.
• It establishes ordering correctness and stability with provable bounds (ordering error <0.003 per edge per cycle) through precise topological and weighted phase assignments.
• Empirical evaluations show that PSMAS outperforms learned routing baselines by decoupling scheduling and compression, yielding up to 27.3% token savings with minimal performance drop.

Phase-Scheduled Multi-Agent Systems for Token-Efficient Coordination

Introduction and Motivation

"Phase-Scheduled Multi-Agent Systems for Token-Efficient Coordination" (2604.17400) addresses a central bottleneck in multi-agent systems (MAS) constructed from LLMs: token inefficiency due to unstructured parallel agent activation and exhaustive context sharing. This inefficiency drives token consumption to $\mathcal{O}(nL)$, where $n$ is the number of agents and $L$ the context length—escalating further as context size grows with agent population. Existing solutions such as static context pruning, hierarchical decomposition, and learned routing fail to tackle the temporal dimension of redundancy, treating routing as a purely structural allocation problem. The critical contribution of this work is to recast agent activation as a continuous control process over a shared attention manifold, delivering formal guarantees of correctness, stability, and efficiency not accessible to prior discrete scheduling heuristics.

Theoretical Framework: Control over the Circular Manifold

The core mechanism of PSMAS is the geometric allocation of activation capacity on the circular manifold $S$, parameterized by a topologically-informed angular "phase" for each agent. A global sweep signal rotates at a configurable velocity, activating agents whose phases fall within a prescribed angular window. Inactive agents receive compressed context summaries, decoupling token savings from the effectiveness of the compression model itself.

The necessity of $S$ over alternatives (e.g., linear slots or discrete rings) is rigorously justified:

• Intrinsic periodicity: Circular scheduling avoids the endpoint discontinuities of linear schedules and aligns with the iterative nature of LLM pipelines.
• Scale-invariant proximity: Circular distance provides a natural metric between activation phases, robust to varying sweep velocities.
• Analytical tractability: The circular structure admits application of dynamical systems theory, specifically the driven Kuramoto model, enabling formal stability and convergence analysis.

These properties are established as uniquely satisfied by $S$ among one-dimensional manifolds.

Algorithmic Implementation

Phase assignment is derived either by topological sort (TPA) or scaled by agent latency (WPA), ensuring ordering constraints required by dependency graphs. Activation is controlled by the sweep signal, with window width $\epsilon$ modulating the degree of parallelization. Context delivery is bifurcated: active agents observe the full context, while inactive agents are relegated to compressed summaries (typically with $\alpha\approx0.12$ compression ratio via Mistral-7B-Instruct).

Token cost per step follows:

$$C_\text{PSMAS}(t) = nL(t) \left[ f(\epsilon) + (1 - f(\epsilon))\alpha \right] + f(\epsilon) n \bar{R}$$

where $f(\epsilon) = \epsilon / 2\pi$ is the active fraction.

Analytical and Empirical Results

The paper provides strong formal results:

• Ordering correctness: With appropriate velocity and phase assignment, the sweep respects dependency constraints with high probability even in the presence of inference latency noise.
• Stability and convergence: Lyapunov-based analyses guarantee convergence to the fixed point of full-activation context and sharply bound quality degradation in terms of $n$0.
• Token reduction bounds: Analytical decomposition confirms that scheduling and compression act independently; strict scheduling alone yields 18-20 percentage points token reduction regardless of compression fidelity ($n$1).

Empirically, evaluated on HotPotQA-MAS, HumanEval-MAS, ALFWorld-Multi, and WebArena-Coord, PSMAS achieves an average token reduction of 27.3% (range: 21.4–34.8%) while incurring a performance drop of less than 2.1pp relative to full activation. Notably, PSMAS-WPA outperforms state-of-the-art adaptive routing baselines such as RouterLLM-RA by 5.6pp in token reduction and 2.0pp in quality deterioration, with significance at $n$2.

In settings lacking explicit dependency structures (unstructured, e.g., dynamic conversational agents), performance gracefully degrades: savings of 14–19% are typical, with minor increases in performance drop (2.9–3.1pp), as the inability to exploit task topology necessitates wider sweep windows and occasional graph inference overheads.

Robustness and Failure Modes

The paper systematically identifies failure modes:

• Phase Misalignment: Errors in the dependency graph can violate ordering; mitigation is via conservative sweep velocities and graph inferencing.
• Velocity Overshoot: Excessive sweep speed relative to agent latency variance induces ordering violations; recommended use of adaptive PI controllers.
• Convergence Stall: Cyclic dependencies in the task graph can stall convergence; resolved via graph restructuring.

These analyses are quantified with probabilistic bounds and practical mitigation strategies.

Implementation and Practical Overhead

Integration with LangGraph requires minimal code augmentation, leveraging a summarisation backend served by vLLM. Scheduling overhead is less than 1.2 seconds per task—substantially less than the inference time savings realized by reduced token and context load (typically 8+ seconds benefit).

Theoretical and Practical Implications

The theoretical implications are twofold:

• The introduction of geometric, temporally continuous control transforms agent scheduling from ad hoc heuristics into analyzable, optimizable systems with explicit connections to dynamical systems literature (driven Kuramoto oscillators).
• The work demonstrates that scheduling-based token savings are robust to imperfections in compression, reorienting future research toward principled temporal coordination over further advances in compression.

Practically, PSMAS offers a ready path to deploying scalable MAS architectures with substantially reduced operational cost, especially in structured domains with explicit dependency graphs. Its performance in unstructured domains, though less dramatic, still surpasses alternative approaches.

Future Trajectories

Potential research directions include adaptive sweep velocity controllers, learned phase assignments using GNNs, extensions to higher-dimensional scheduling manifolds (e.g., tori for simultaneously structured tasks), memory-augmented idle agents, and real-time task graph inference to close the structured-unstructured efficacy gap.

Conclusion

PSMAS establishes a new paradigm for coordination in LLM-based MAS by leveraging continuous, geometric control principles. It achieves substantial token economy with minimal quality tradeoff and provides analytic guarantees absent in prior heuristic schemes. Its framework, grounded in circular manifold dynamics, sets a new standard for scalable, efficient, and analyzable multi-agent orchestration in both structured and unstructured AI settings.