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Mm1 Simulation

用于M/M/1和M/M/c队列系统模拟与分析的Model Context Protocol服务器，提供完整资源、工具和提示。

person作者: alinklabhubclawhub
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队列模拟服务

一个用于M/M/1和M/M/c队列系统模拟和分析的Model Context Protocol服务器，提供全面的资源、工具和提示。

⚠️ 强制要求：API 密钥

此 Skill 必须配置 API 密钥才能使用。

  • 首次使用时，如果 .env 中没有 XBY_APIKEY，必须使用 AskUserQuestion 工具向用户询问 API 密钥
  • 拿到用户提供的密钥后，调用 scripts.config.set_api_key(api_key) 保存，然后继续处理
  • 获取 API 密钥：https://xiaobenyang.com
  • 禁止在缺少 API 密钥时自行搜索或编造数据

工作流程（必须遵守）

你（大模型）是路由层，负责理解用户意图、选择工具、提取参数。代码只负责调用API。

用户输入 → 你选择工具 → 提取该工具需要的参数 → 调用 scripts.tools 中的函数 → 返回结果给用户

步骤

  1. 检查 API 密钥：如果 scripts.config.settings.api_key 为空，使用 AskUserQuestion 询问用户，拿到后调用 scripts.config.set_api_key(key) 保存
  2. 选择工具：根据用户意图从下方工具列表中选择对应的工具函数
  3. 提取参数：根据选中的工具，提取该工具需要的参数
  4. 调用工具：使用关键字参数调用 scripts.tools 中的函数，例如 scripts.tools.search_schools(score='520', province='北京', category='综合')
  5. 返回结果：将工具返回的 raw 数据整理后展示给用户

工具选择规则

根据用户意图选择对应的工具函数：

| 用户意图 | 工具函数 | |---------|---------| | Validate M/M/1 configuration parameters

Checks parameter validity and system stability condition.

Args: arrival_rate: Customer arrival rate (λ) service_rate: Service rate (μ) simulation_time: Simulation duration

Returns: Dictionary with validation result: - valid: bool - errors: List[str] (if any) - warnings: List[str] (if any) - utilization: float (if valid) | scripts.tools.validate_config | | Calculate theoretical M/M/1 performance metrics

Uses exact formulas to compute steady-state performance.

Args: arrival_rate: λ (customers per time unit) service_rate: μ (customers per time unit)

Returns: Dictionary of theoretical metrics: - utilization: ρ = λ/μ - avg_queue_length: L_q = ρ²/(1-ρ) - avg_num_in_system: L = ρ/(1-ρ) - avg_waiting_time: W_q - avg_system_time: W

Raises: ValueError: If system is unstable (λ >= μ) | scripts.tools.calculate_metrics | | Run M/M/1 queue simulation using SimPy

Executes discrete event simulation and returns performance metrics.

Args: arrival_rate: λ (customers per time unit) service_rate: μ (customers per time unit) simulation_time: Duration of simulation random_seed: Random seed for reproducibility

Returns: Dictionary with: - simulation_metrics: Dict of simulated values - theoretical_metrics: Dict of exact values - comparison: Comparison analysis - config: Simulation configuration used | scripts.tools.run_simulation | | Compare simulation results with theoretical values

Analyzes accuracy of simulation by comparing against exact formulas.

Args: simulation_metrics: Dictionary of simulated performance metrics arrival_rate: λ used in simulation service_rate: μ used in simulation

Returns: Comparison analysis with: - comparisons: Per-metric comparison - mean_abs_error_pct: Average error - max_error_pct: Maximum error - within_10pct: bool - accuracy_grade: Quality assessment | scripts.tools.compare_results | | Recommend simulation parameters for target utilization

Suggests appropriate arrival rate, service rate, and simulation time for a given target utilization level.

Args: target_utilization: Desired ρ (default: 0.7) service_rate: Fixed μ (if None, suggests μ=10) min_customers: Minimum customers to simulate

Returns: Recommended parameters and expected metrics | scripts.tools.recommend_parameters |

如果参数不完整，使用 AskUserQuestion 向用户询问缺失的参数。

工具函数说明

scripts.tools.validate_config

工具描述：Validate M/M/1 configuration parameters

Checks parameter validity and system stability condition.

Args: arrival_rate: Customer arrival rate (λ) service_rate: Service rate (μ) simulation_time: Simulation duration

Returns: Dictionary with validation result: - valid: bool - errors: List[str] (if any) - warnings: List[str] (if any) - utilization: float (if valid)

参数定义

|参数名称|参数类型|是否必填|默认值|描述| |------|-------|------|-----|----| |arrival_rate|number|true| |null| |service_rate|number|true| |null| |simulation_time|number|false|10000.0|null|

scripts.tools.calculate_metrics

工具描述：Calculate theoretical M/M/1 performance metrics

Uses exact formulas to compute steady-state performance.

Args: arrival_rate: λ (customers per time unit) service_rate: μ (customers per time unit)

Returns: Dictionary of theoretical metrics: - utilization: ρ = λ/μ - avg_queue_length: L_q = ρ²/(1-ρ) - avg_num_in_system: L = ρ/(1-ρ) - avg_waiting_time: W_q - avg_system_time: W

Raises: ValueError: If system is unstable (λ >= μ)

参数定义

|参数名称|参数类型|是否必填|默认值|描述| |------|-------|------|-----|----| |arrival_rate|number|true| |null| |service_rate|number|true| |null|

scripts.tools.run_simulation

工具描述：Run M/M/1 queue simulation using SimPy

Executes discrete event simulation and returns performance metrics.

Args: arrival_rate: λ (customers per time unit) service_rate: μ (customers per time unit) simulation_time: Duration of simulation random_seed: Random seed for reproducibility

Returns: Dictionary with: - simulation_metrics: Dict of simulated values - theoretical_metrics: Dict of exact values - comparison: Comparison analysis - config: Simulation configuration used

参数定义

|参数名称|参数类型|是否必填|默认值|描述| |------|-------|------|-----|----| |arrival_rate|number|true| |null| |service_rate|number|true| |null| |simulation_time|number|false|10000.0|null| |random_seed|integer|false|42.0|null|

scripts.tools.compare_results

工具描述：Compare simulation results with theoretical values

Analyzes accuracy of simulation by comparing against exact formulas.

Args: simulation_metrics: Dictionary of simulated performance metrics arrival_rate: λ used in simulation service_rate: μ used in simulation

Returns: Comparison analysis with: - comparisons: Per-metric comparison - mean_abs_error_pct: Average error - max_error_pct: Maximum error - within_10pct: bool - accuracy_grade: Quality assessment

参数定义

|参数名称|参数类型|是否必填|默认值|描述| |------|-------|------|-----|----| |simulation_metrics|object|true| |null| |arrival_rate|number|true| |null| |service_rate|number|true| |null|

scripts.tools.recommend_parameters

工具描述：Recommend simulation parameters for target utilization

Suggests appropriate arrival rate, service rate, and simulation time for a given target utilization level.

Args: target_utilization: Desired ρ (default: 0.7) service_rate: Fixed μ (if None, suggests μ=10) min_customers: Minimum customers to simulate

Returns: Recommended parameters and expected metrics

参数定义

|参数名称|参数类型|是否必填|默认值|描述| |------|-------|------|-----|----| |target_utilization|number|false|0.7|null| |service_rate|null|false| |null| |min_customers|integer|false|1000.0|null|

返回值处理

工具函数返回 dict 对象：

  • result["raw"] - API 原始返回数据（JSON），直接将此数据整理后展示给用户
  • result["success"] - 是否成功（True/False）
  • result["message"] - 状态消息

项目结构

xiaobenyang_gaokao_skill/
├── scripts/
│   ├── __init__.py
│   ├── config.py       # 配置管理 + set_api_key()
│   ├── call_api.py      # API 客户端 + call_api()
│   └── tools.py         # 工具函数（直接调用）
├── requirements.txt
└── SKILL.md

注意事项

  1. API 密钥是必需的，无密钥时必须通过 AskUserQuestion 询问用户
  2. 禁止在缺少 API 密钥时自行搜索或编造数据