Agent Mars Performance Index (AMPI)

• AMPI is a composite metric designed to quantify multi-agent coordination in Mars base operations with emphasis on efficiency, communication, and reliability.
• It aggregates five sub-metrics—time, messages, cross-layer ratio, failures, and role switches—using configurable normalization and weighting to yield an interpretable single score.
• Its modular structure and clear design principles enable benchmarking and optimization of coordination policies under extreme resource and safety constraints.

The Agent Mars Performance Index (AMPI) is a composite metric designed to quantify the operational effectiveness, communication efficiency, robustness, and resilience of multi-agent teams coordinating under the unique constraints of Mars base operations. It formalizes performance assessment in environments featuring heterogeneous agents (humans, robots, software services), strict safety mandates, extreme resource scarcity, and intermittent communications. AMPI is structured as an interpretable, single-number score, integrating five diagnostically meaningful sub-metrics: execution speed, inter-agent communication, cross-layer routing, operational failure rates, and dynamic redundancy via role switching. With explicit modularity, normalization, and configurability, AMPI enables principled comparison, benchmarking, and optimization of coordination policies within high-fidelity Mars simulation environments (Wang, 9 Feb 2026).

1. Rationale and Design Principles

AMPI was introduced to address the evaluation gap in large-scale, safety-critical, multi-agent settings such as Mars base operations, where traditional single-agent or narrow multi-agent metrics are insufficient. Its design targets four key system properties:

• Efficiency: Captures rapidity of convergence to mission objectives.
• Communication Overhead: Quantifies messaging volume and network load (“chatty-ness”).
• Reliability: Measures operational success via avoidance of component failures and constraint violations.
• Resilience: Evaluates capacity to maintain function under outages via dynamic asset-control handovers.

The metric’s construction is guided by strict monotonicity (better performance always maps to higher AMPI), modularity (optional cross-layer penalty), interpretability (all components reported and analyzed separately), and configurability (user-determined weighting and saturation constants for mission-adaptive emphasis).

2. Mathematical Formulation

AMPI aggregates five core sub-metrics, computed on each scenario run:

Symbol	Measure	Raw Value Definition
$T$	Time	End-to-end wall-clock runtime (seconds)
$M$	Messages	Total number of inter-agent messages exchanged
$C$	Cross-layer ratio	Fraction of messages traversing cross-layer hops
$F$	Failures	Sum of asset failures, constraint violations, and missing deliverables
$S$	Role switches	Number of asset-control role handovers

Non-ratio quantities ($T, M, F, S$) are normalized using a monotonic “squash” function:

$\tilde X = \frac{X}{X + K_X}$

where $K_X > 0$ sets the half-saturation point and is user-configurable. By default, $K_T=20$ s, $K_M=50$ msgs, $M$0 failures, $M$1 switches. The cross-layer term $M$2 is inherently bounded to $M$3 and is not normalized further.

AMPI is computed as:

$M$4

with $M$5 and $M$6. Default weights: $M$7. By default, no penalty is applied for cross-layer communication (i.e., $M$8); this can be enabled to enforce stricter hierarchy.

3. Sub-Metric Definitions and Roles

Time (T)

• Definition: Scenario wall-clock runtime (seconds), or optionally, surrogate measures of computational effort (e.g., $M$9 for LLM queries).
• Normalization: $C$0.
• Interpretation: Lower times indicate faster plan convergence; higher $C$1 yields higher AMPI.

Messages (M)

• Definition: Total count of inter-agent messages.
• Normalization: $C$2.
• Interpretation: Lower values reflect lower communication overhead.

Cross-layer Ratio (C)

• Definition: $C$3, where $C$4 is the number of whitelisted cross-layer messages and $C$5 is the total number of messages.
• Normalization: Not applied ($C$6).
• Interpretation: Optionally penalizes excess cross-layer routing, according to mission policy.

Failures (F)

• Definition: Aggregated event count: asset unserviceabilities ($C$7), violation of operational/safety constraints ($C$8), and missing deliverables ($C$9): $F$0.
• Normalization: $F$1.
• Interpretation: Robustness indicator; fewer failures directly increase AMPI.

Role Switches (S)

• Definition: Number of asset-control handovers caused by controller outages.
• Normalization: $F$2.
• Interpretation: Quantifies dynamic redundancy overhead; interpreted in the context of reliability trade-offs.

4. Practical Implementation and Computation

During each scenario run, a centralized “metrics” module logs all messages, classifies cross-layer hops, records outage-induced handovers, flags violations, and tracks deliverable completion status. At run-end, the collected totals ($F$3) are exported (typically as CSV). Any missing or incomplete logs default to maximum penalty (e.g., missing deliverable is always counted as a failure). For variable latency environments or alternative evaluation regimes, substitute measures such as $F$4 or $F$5 can replace $F$6, with corresponding adjustments to $F$7.

The cross-layer ratio penalty is disabled by default, but can be selectively enabled via runtime flags, permitting targeted study of hierarchical versus cross-functional operational doctrine.

5. Example Calculation from Operational Scenarios

Representative results are summarized for scenarios such as “DailyOperations” under strictly hierarchical (“STRICT”) routing with a single leader, and under cross-layer functional leadership. For example:

Scenario	$F$8 (s)	$F$9	$S$0	$S$1	$S$2	AMPI (default)
DailyOperations, STRICT	232.4	43	0.00	0.06	1.20	0.50
DailyOperations, CROSSLAYER/functional	191.9	42	0.10	0.05	0.90	0.52

In the STRICT routing run:

$S$3

Resulting in $S$4.

Under functional leadership and enabled cross-layer routing, improved time and lower failures increased AMPI to $S$5 despite a small cross-layer penalty. This demonstrates AMPI’s utility in diagnosing trade-offs in operational doctrine.

6. Interpretation and Application

The AMPI score ranges from 0 (maximal overhead, failures, and redundancy with minimum efficiency) to 1 (optimal execution, minimum messaging, no failures, no role switches). It is recommended to report not only aggregated AMPI but also all five normalized sub-metrics to dissect causes of performance changes across scenario variants. Weighting and normalization parameters should be listed in any published analysis to ensure reproducibility.

AMPI is designed for direct comparability across control policies, leadership modes, routing algorithms, and consensus/memory protocol configurations, including ablation and cross-layer experimental settings. Adjustments to weights or normalization points should be performed to reflect mission-phase priorities, such as emphasizing reliability ($S$6) in emergency preparedness phases.

7. Extensions and Best Practices

AMPI’s modular, auditable formulation supports extension to alternative domains requiring unified efficiency-robustness diagnostics beyond Mars base simulation. Practitioners are advised to carefully document scenario configurations—seed prompts, outage rates, protocol settings, AMPI weights and saturation constants, and statistical variability—for benchmarking and cross-study comparison.

In summary, the Agent Mars Performance Index offers a compositional, configurable, and interpretable foundation for benchmarking large-scale, safety-critical, multi-agent coordination in extraterrestrial environments, directly supporting advanced study of layered command structures, functional leadership, and communication protocols in auditable Space AI systems (Wang, 9 Feb 2026).