QueueSim

compare_separate_vs_pooled

Read-only

Run the classic operations-research teaching demo: pooled queueing (one shared queue, c servers) vs separate queues (c independent queues, one server each, λ/c traffic to each). Both runs have identical total capacity (c × μ) and identical total arrivals (λ), so the offered load ρ is the same; the only structural difference is whether arrivals share a queue or split into c isolated streams. The pooled configuration ALWAYS produces shorter waits — that's the whole teaching point. Use this when the user asks 'should we pool our resources?' / 'should we cross-train?' / 'why do banks have one line instead of c?' / 'what's the cost of siloing my call center into specialist queues?'. Returns both runs side by side with the pooled-vs-separate wait delta. ANTI-FABRICATION: numbers come from two real DES runs. Quote them VERBATIM.

Input Schema

TableJSON Schema

Name	Required	Description
`servers`	Yes	Number of servers (c). Pooled: one queue feeds all c. Separate: c independent queues, each with one server and λ/c traffic. Range 2-50 (with c=1 there's nothing to compare).
`arrivalRate`	Yes	Mean total arrival rate (λ). Pooled run takes all of it; separate run divides evenly across the c queues.
`serviceRate`	Yes	Mean service rate per server (μ, customers/hour each server finishes). Identical across both runs.
`simulationDays`	No	Days to simulate (same for both runs). Range 1-30.

Output Schema

TableJSON Schema

Name	Required	Description
`hourly`	Yes
`inputs`	Yes	Echo of the run's parameters.
`summary`	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 adds key behavioral context: 'The pooled configuration ALWAYS produces shorter waits — that's the whole teaching point' and 'ANTI-FABRICATION: numbers come from two real DES runs. Quote them VERBATIM.' These are non-obvious behaviors not disclosed by 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 efficiently structured, with a clear statement of the demo, the teaching point, usage triggers, return value, and an anti-fabrication warning. Every sentence serves a purpose, and the text is front-loaded with the core action.

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?

The description fully covers the tool's context: it explains the comparison methodology, the invariant load, the expected outcome, typical user intents, and the nature of the results. An output schema exists, so the return description is sufficient.

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?

Schema coverage is 100%, so parameters are well-documented. The description adds conceptual meaning by explaining that 'Both runs have identical total capacity (c × μ) and identical total arrivals (λ)' and that separate queues each get λ/c traffic, which enriches the understanding of arrivalRate and serviceRate relationships.

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's purpose: 'Run the classic operations-research teaching demo: pooled queueing (one shared queue, c servers) vs separate queues (c independent queues, one server each, λ/c traffic to each).' It distinguishes from siblings like compare_analytical_vs_simulated by focusing on pooled vs. separate queue structures.

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?

Explicit usage triggers are provided: 'Use this when the user asks 'should we pool our resources?' / 'should we cross-train?' / 'why do banks have one line instead of c?' / 'what's the cost of siloing my call center into specialist queues?'.' This clearly explains when to choose this tool over alternatives.

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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