# Ramen Shop Queue Estimator AI Agent Connect

> Predict wait times and congestion for Japanese-style ramen shops using queueing theory.

## Overview
- **Category:** business
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_VfXuDoQ2QX7dKYcAuiJKda2gadlKJWXxzthVIQWH/ai-agent-connect
- **Tags:** queueing-theory, retail, operations, ramen, wait-time

## Description

This MCP server provides deterministic modeling for ramen shops with individual booth service. It uses Little's Law and M/M/c queueing approximations to provide accurate operational insights. Use `get_service_metrics` to monitor shop capacity and congestion, `estimate_wait_time` to predict how long customers in line will wait, and `predict_probability_of_delay` to assess the likelihood of significant delays.

## Tools

### estimate_wait_time
Predicts how long a customer currently in line will wait before being seated

### get_service_metrics
Provides fundamental capacity and utilization metrics for the shop

### predict_probability_of_delay
Estimates the likelihood that a customer will face a significant delay

## Prompt Examples

**Prompt:** 
```
How busy is the shop right now with 10 booths, 20 minute eating time, and 5 customers arriving per hour?
```

**Response:** 
```
The shop has a service rate of 30 customers per hour, resulting in a utilization of 0.16. There is no extreme congestion.
```

**Prompt:** 
```
How long will a customer wait if there are 5 booths, 15 minute eating time, and 10 people are in line?
```

**Response:** 
```
The expected wait time for the customer at the front of the queue is 30 minutes.
```

**Prompt:** 
```
What is the chance of a wait longer than 30 minutes with 8 booths, 20 minute eating time, and 20 customers per hour?
```

**Response:** 
```
The probability of a wait exceeding 30 minutes is 0.12.
```

## Frequently Asked Questions

**How does this tool calculate wait times?**
The tool uses the number of available booths and the average eating time to determine the service rate, then applies queueing theory to estimate wait times based on the current queue length.

**What is considered extreme congestion?**
Extreme congestion is flagged when the utilization rate exceeds 0.9, meaning the arrival rate is very close to the maximum service capacity.

**Can I use this for any restaurant?**
While designed for booth-style service like Ichiran, the mathematical models can be applied to any service environment with discrete service stations.