QueueSim

compare_analytical_vs_simulated

Read-only

Run the same M/M/c configuration through BOTH the closed-form Erlang-C formula AND the discrete-event simulator, returning a side-by-side comparison with deltas. Use this when the user is validating QueueSim's engine against textbook values, learning queueing theory by watching simulation converge on the formula, or auditing a result that 'feels off' — agreement within ~5%% is the canonical sanity check for an M/M/c run. Pure-Exponential M/M/c only; the closed-form Erlang-C is undefined for other service distributions. Large deltas usually mean the simulation run was too short for steady-state — raise simulationDays. ANTI-FABRICATION: both sides come from real computation — closed-form is deterministic, simulation is stochastic but engine-backed. Quote both verbatim. Do not synthesize an 'average of the two' or recompute the formula from training-data recall.

Input Schema

TableJSON Schema

Name	Required	Description
`servers`	Yes	Number of parallel servers (c). Integer 1-50.
`arrivalRate`	Yes	Mean arrivals per hour (λ).
`serviceRate`	Yes	Mean customers one server can finish per hour (μ). Must be > 0.
`simulationDays`	No	Days to simulate on the DES side. Closed-form is instant. Range 1-30; longer runs converge closer to the formula.

Output Schema

TableJSON Schema

Name	Required	Description	Default
`note`	No
`delta`	Yes
`inputs`	Yes
`simulated`	Yes
`analytical`	Yes

TDQS

A4.9/5.0

Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Beyond the readOnlyHint and destructiveHint annotations, the description discloses key behavioral traits: 'closed-form is deterministic, simulation is stochastic but engine-backed,' the anti-fabrication rule to quote both verbatim, and the troubleshooting hint that large deltas mean simulation too short. It also warns against synthesizing averages or recomputing from training-data recall. This provides substantial behavioral context beyond annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is front-loaded with a clear purpose statement, followed by when-to-use, constraints, troubleshooting, and anti-fabrication rules. Every sentence carries important information without redundancy. The length is justified by the tool's complexity and the critical behavioral guidance needed for correct usage.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool has an output schema and 4 well-documented parameters, the description covers purpose, usage scenarios, exclusions, troubleshooting, and behavioral expectations. It explicitly notes the pure-M/M/c limitation and how to react to large deltas. With annotations and output schema already providing structured metadata, this description is fully complete for an AI agent to select and invoke the tool correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema already documents all 4 parameters with 100% coverage, so the baseline is 3. The description adds value by tying the 'simulationDays' parameter to a troubleshooting scenario ('raise simulationDays' for large deltas) and confirms the M/M/c scope for the service distribution. This incremental guidance justifies a score above baseline.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool runs the same M/M/c configuration through both the Erlang-C formula and the discrete-event simulator, returning a side-by-side comparison with deltas. It uses a specific verb ('Run'), names the exact resources, and is easily distinguished from siblings like 'compare_separate_vs_pooled' or 'simulate_mmc'.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explicitly says when to use this tool: 'validating QueueSim's engine against textbook values, learning queueing theory... or auditing a result that feels off.' It also provides an exclusion criterion: 'Pure-Exponential M/M/c only; the closed-form Erlang-C is undefined for other service distributions.' This gives clear when-to-use and when-not-to-use guidance.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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TDQS

A4.7/5.0

Disambiguation5/5

Each tool has a clearly distinct purpose: simulation (simulate_mmc, simulate_scenario, simulate_schedule), comparison (compare_analytical_vs_simulated, compare_separate_vs_pooled), inverse analysis (recommend_staffing), interpretation (interpret_result), education (explain_queueing_theory, explain_advanced_patterns), and scenario management (list_scenarios, describe_scenario). No two tools overlap significantly, and nuanced differences are explicitly documented (e.g., when to use simulate_mmc vs simulate_scenario).

Naming Consistency5/5

All tool names follow a consistent verb_noun pattern in snake_case: compare_*, describe_*, explain_*, interpret_*, list_*, recommend_*, simulate_*. Even compound names like compare_analytical_vs_simulated are clearly structured and match the pattern. There are no mixed conventions or vague verbs.

Tool Count5/5

11 tools is well within the ideal 3-15 range and each tool earns its place. The set covers simulation, comparison, recommendation, interpretation, education, and scenario discovery without redundancy or bloat. The count feels right for a queueing theory teaching and simulation server.

Completeness5/5

The tool surface is complete for its stated domain: it offers multiple simulation modes (generic, preset, custom schedule), an inverse staffing finder, analytical-vs-simulation comparison, pooled-vs-separate comparison, interpretation, and educational explainers. There are no obvious dead ends—users can model, validate, understand, and optimize queueing scenarios. The intentional exclusion of advanced pattern simulation is addressed by explain_advanced_patterns pointing to ChiAha.

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