✨ Educational Queue Management System

Your queues,
optimized with purpose.

Discover how math and technology can predict dining hall crowds, reduce wait times, and make every moment count.

50%
Reduced Wait Time
3
Prediction Models
24/7
Real-time Updates
🎯

Why This Matters

Every minute spent waiting in line is a minute lost from your day. Our tools use real mathematics to help you understand queue behavior, predict busy times, and make smarter decisions about when to grab lunch.

What Can You Do Here?

Explore powerful tools that show you how queues work and help predict the best times to visit the dining hall.

Simulation

Run Simulations

Play with virtual queues! Change the number of servers and see how it affects wait times in real-time.

Forecast

Predict the Future

Use AI models to forecast how busy the dining hall will be tomorrow, next week, or any time!

Scenarios

Compare Scenarios

What if we added more staff? Compare different setups and find the best solution.

Glossary

Learn the Terms

Queuing theory sounds fancy, but it's simple! Learn all the key terms in plain language.

How Does It All Work?

From collecting data to predicting wait times, here's the journey of how QueueSmart helps students.

1 Data Collection (Conceptual Design)

This project demonstrates how sensors could work at dining hall entrances to count people. In this educational implementation, we use synthetic data and simulation models instead of real sensors.

The synthetic data generator creates realistic arrival patterns based on theoretical distributions, allowing us to test and demonstrate queueing theory concepts.

📊 Theory
→
🔧 Generator
→
💾 Synthetic Data

Simulated data based on theoretical arrival distributions

2 Queueing Theory (M/M/s)

This is the math that makes it all work! M/M/s is a formula that predicts how long you'll wait based on three things:

  • M - How often people arrive (randomly)
  • M - How long it takes to serve each person
  • s - Number of servers (checkout stations)
λ = 5/min
Arrival Rate
μ = 2/min
Service Rate
s = 3
Servers
ρ = λ/(s×μ) = 83%

3 Forecasting with AI

We use two smart prediction methods:

ARIMA - Like a weather forecast for crowds! It finds patterns (like "Tuesdays are always busy") and predicts future trends.

LSTM - A neural network (AI brain) that learns from weeks of data to spot complex patterns humans might miss.

📊 Past Data
→
🧠 AI Model
→
🔮 Prediction
📈
ARIMA
🤖
LSTM
🎯
Hybrid

4 Dashboard & Decisions

All this data comes together in an easy-to-read dashboard that helps:

  • Students - Know the best time to eat
  • Staff - Know when to add more servers
  • Managers - Plan better schedules
📱

Real-time updates on your phone or computer

Low Wait
Moderate
Busy
🎮

Why Simulation Matters

Real experiments are expensive and time-consuming. With simulation, you can test hundreds of "what-if" scenarios in seconds - no real customers needed! It's like having a practice mode for your dining hall.

🎮 Queue Simulation Lab

Adjust the sliders and see how different settings affect wait times!

🎢 Think of it like a roller coaster line...

Imagine you're at an amusement park. The arrival rate is how many people join the line each minute. The service rate is how fast the ride loads passengers. And the number of servers is like having multiple loading stations. More loading stations = shorter waits!

⚙️ What-If Controls

Drag sliders OR type exact values - they stay in sync!

How many customers arrive per hour during rush
Average minutes to serve one customer
Number of checkout stations or servers
How long to run the simulation (like movie length)
More runs = more accurate results (averaging out randomness)

📊 Results

--
Avg Wait (min)
--
Total Time (min)
--
Utilization
--
Served/Hour
Adjust the sliders and click "Run Simulation" to see results!

📜 Simulation History

Your simulation results will appear here

🔮

Why Prediction Matters

Knowing the future lets you prepare! Staff can be scheduled when needed most, and students can plan their meals around the quietest times. It's the difference between waiting 2 minutes and waiting 20.

🔮 Arrival Forecast

See into the future! Predict how busy the dining hall will be.

🌤️ Why Forecasting Matters

Just like checking the weather before a picnic, forecasting crowd levels helps you plan your day better. Would you rather show up when there's a 5-minute wait or a 30-minute line? With predictions, you can pick the perfect time to grab lunch!

📈 ARIMA

Pattern detective! Finds trends and cycles in past data.

🧠 LSTM

AI brain that learns complex patterns over time.

🎯 Hybrid

Best of both! Combines ARIMA and LSTM predictions.

Predicted Arrivals

⚙️ Forecast Settings

Peak Hour --
Lowest Hour --
Model Used ARIMA

📚 Understanding the Models

📈 ARIMA Explained

ARIMA stands for "Auto-Regressive Integrated Moving Average." It's like having a really smart friend who remembers every Tuesday lunch rush and can predict next Tuesday will be similar. It looks for:

  • Daily patterns (lunch is always busy)
  • Weekly patterns (Mondays differ from Fridays)
  • Trends (getting busier over time?)

🧠 LSTM Explained

LSTM is a type of artificial neural network - basically a computer program that learns like a brain! It's great at remembering important things from weeks ago while ignoring random noise. Think of it like:

  • A student who studies for weeks
  • Remembers what matters for the test
  • Forgets unimportant details
⚖️

Why Comparison Matters

Every decision has trade-offs. Adding more servers costs money but reduces wait times. This tool helps you find the sweet spot - the perfect balance between cost and customer satisfaction.

⚖️ Scenario Comparison

What if we changed things? Compare different staffing plans!

🏫 Think of a university dining hall...

During lunch rush (11:30am-1pm), hundreds of hungry students flood in! With only a few stations open, lines stretch out the door. But open more serving lines, and suddenly everyone gets their food quickly. This tool helps you find the sweet spot!

🎛️ Configure Your Scenario

Drag sliders OR type exact values - designed for real university dining hall operations!

Peak lunch: 600-1000+, game days: 1500+
Grab-n-go: 1-2 min, full meal: 4-8 min, made-to-order: 10-20 min
Large dining hall: 20-40 stations across all lines
Proposed capacity with extra lines open during rush
Baseline Utilization: --
Improved Utilization: --
Min Servers Needed: --
BASELINE

Current Setup

Servers 5
Avg Wait --
Utilization --
Throughput --
IMPROVED

Proposed Setup

Servers 7
Avg Wait --
Utilization --
Throughput --
📖

Why Learning Terms Matters

Understanding the vocabulary of queueing theory unlocks a whole new way of thinking about everyday situations - from grocery stores to hospitals. These concepts apply everywhere lines form!

📖 Queue Glossary

Learn the language of queues! These terms might sound fancy, but they're actually simple concepts you see every day.

📥

Queue

A line of people waiting for service. Just like the lunch line at school!

The word "queue" comes from the French word for "tail" - like the tail end of a line!
🚶

Arrival Rate (λ)

How many people join the line per minute or hour. Symbol: λ (Greek letter "lambda")

At peak lunch time, a busy dining hall might see 3-5 people arrive every minute!
⚡

Service Rate (μ)

How fast each server can help people. Symbol: μ (Greek letter "mu")

A fast food cashier can serve about 20-30 customers per hour!
📊

Utilization (ρ)

How busy the servers are, shown as a percentage. 80% means servers are busy 80% of the time.

Too high (95%+) means long waits. Too low (50%-) means wasted resources!
⏱️

Wait Time (Wq)

How long you wait in line before being served. The "q" stands for "queue".

Studies show people overestimate wait times by 36% when they're bored!
🔄

System Time (W)

Total time from joining the line until you're done being served. Wait time + service time!

Disney uses clever distractions to make system time feel shorter!
👥

Queue Length (Lq)

Average number of people waiting in line at any moment.

The longest recorded line was for iPhone 5 release - over 400 people!
🎰

M/M/s Model

A math formula for queues where arrivals and service times are random (Markov), with "s" servers.

This model was invented to help telephone operators in the early 1900s!
📈

Throughput

How many people are served per hour. Higher is better!

Amazon warehouses process over 1 million packages per day!
🧮

Little's Law

A famous formula: L = λ × W (People in system = Arrival rate × Time in system)

Named after John Little who proved it in 1961 - it works for ANY queue!
📞

Erlang C Formula

Calculates the probability you'll have to wait when you arrive.

Named after Danish mathematician Agner Krarup Erlang, the "father of queueing theory"!
🤖

Simulation

A computer program that pretends to be a real queue, running thousands of scenarios to find averages.

Video games use similar simulations to model traffic and crowds!
🎬

Simulation Time (The Movie Length)

How long to run the simulation - like choosing between a short clip or a full-length movie of the queue!

Think of it like watching a movie: A 360-minute simulation is like watching a 6-hour movie of the dining hall - you see breakfast, lunch, and dinner rushes all play out!

Examples:
• 60 min = Just lunch hour 🍕
• 360 min = 6 hours (multiple rush periods) 📊
• 1440 min = Full 24-hour day 🌅➡️🌙

Why it matters: Longer simulations reveal patterns you'd miss in short runs - like the quiet 2pm lull after lunch!
🔄

Number of Runs (The Replay Button)

How many times to repeat the simulation and average the results - like flipping a coin many times to see the true odds!

Think of it like flipping a coin: Flip once, you might get heads. Flip 100 times, you'll see it's about 50-50. Simulation runs work the same way!

Examples:
• 1 run = Could be lucky or unlucky 🎲
• 10 runs = Getting a clearer picture 📈
• 100 runs = Very confident results! ✅

Why it matters: Queues have randomness (customers don't arrive like clockwork). Multiple runs capture this variability and give you confidence in your recommendations!

About QueueSmart

The story of how a frustrating lunch line became an exciting research project.

👨‍🎓

Sanjeev's Story

Industrial Engineering Junior @ Mercer University

Sanjeev was tired of wasting his lunch break in long lines.

Every day at 12:15, he'd rush from his Operations Research class to the dining hall, only to find a line stretching out the door. By the time he got his food, he had 10 minutes left to eat before his next class.

"There has to be a better way," he thought. What if he could predict when the line would be shortest? What if the dining hall knew to open more checkout stations during rush hour?

That question sparked QueueSmart - a system that uses math and AI to help everyone spend less time waiting and more time enjoying their meals.

😤 The Problem

  • Students waste 15-30 minutes waiting in line daily
  • Staff don't know when to add more servers
  • Unpredictable crowd levels cause frustration
  • No data-driven decision making

✨ The Solution

  • Simulation-based queue modeling and analysis
  • AI-powered predictions using synthetic data
  • Staffing recommendations based on queueing theory
  • Interactive dashboard for scenario exploration

📚 Educational Project Note: This is an academic capstone project developed as part of an Operations Research course (Fall 2025).

  • No actual sensors were deployed - the data collection concept is theoretical
  • No real dining hall data was collected - all data is synthetically generated
  • This is a theoretical/academic project using simulations and queueing theory models

What was actually implemented: Queue simulation models (M/M/1, M/M/s, M/M/c), synthetic data generator, ARIMA & LSTM forecasting on synthetic data, interactive dashboard for scenario analysis, and theoretical queueing theory applications.

📅 Project Timeline

August 2025

Research & Planning

Studied queueing theory fundamentals (Lessons 22-25 from Operations Research course). Identified dining hall queue problem and designed initial solution architecture.

September 2025

Network Analysis & Optimization

Applied network flow algorithms and PERT-CPM methodologies. Developed conceptual framework for queue management system.

October 2025

Simulation Data Generation

Built synthetic data generator for simulation purposes. Developed M/M/s analysis tools using simulated arrival/service patterns. Created statistical models based on theoretical distributions.

November 2025

Model Development

Implemented queueing theory models (M/M/1, M/M/s, M/M/c). Trained ARIMA and LSTM forecasting models on synthetic data. Developed discrete-event simulation.

December 2025

Dashboard Launch

Created interactive web dashboard. Integrated all features: simulation, forecasting, scenarios. Final testing, refinement, and project completion.

👨‍💻 About the Developer

👨‍🎓

Sanjeev Raila

Project Lead & Developer

Industrial Engineering Junior at Mercer University (3.77 GPA, Dean's List). Certified Lean Six Sigma Green Belt with proven track record of delivering 15-50% operational improvements. Experienced in operations research, statistical process control, and data-driven decision-making. Currently serving as IISE Chapter President and seeking Summer 2026 IE internship opportunities.

🎓 Education: Bachelor of Science in Industrial Engineering, Mercer University (May 2027)

📧 Email: sanjeev.raila15@gmail.com

🔗 LinkedIn: linkedin.com/in/sanjeev-raila

💰 Cost Optimizer

Find the sweet spot between staffing costs and customer wait times!

⚖️ The Manager's Dilemma...

Every dining hall manager faces this: Hire more staff = happier customers but higher costs. Fewer staff = lower costs but longer lines. This tool uses math to find the PERFECT balance where total costs (staffing + waiting) are minimized!

🧮 Cost Calculator

Enter your costs and system parameters to see the total cost breakdown.

How many customers arrive per hour
How many customers each server can handle per hour
Current number of servers/stations
Hourly wage or cost per server
Value of customer time (lost productivity, dissatisfaction)

🎯 Find Optimal Staffing

Let the algorithm find the number of servers that minimizes total cost!

🔮 Predictive Calculator

Reverse-engineer queueing parameters from observed performance!

🔍 Work Backwards Like a Detective...

Sometimes you know the result but not the cause! If customers wait 5 minutes on average, how many are arriving? If you have 10 servers, what service speed do you need? This calculator uses numerical methods to solve these "reverse" problems!

🔄 Choose What to Estimate

What You Know:

You've observed the average wait time, you know how many servers you have and their service rate. Find out how many customers must be arriving!

Average time customers spend waiting in line
How many service stations are open
Customers each server can handle per hour

📚 The Math Behind It

Standard queueing theory gives us formulas like Wq = f(λ, μ, c) where wait time depends on arrival rate, service rate, and servers. These equations are implicit and can't be solved algebraically for the inputs. We use Brent's numerical method to find the root: given a target Wq, iterate until f(x) - Wq = 0!

📬 Get in Touch

Have questions, suggestions, or want to bring QueueSmart to your school? I'd love to hear from you!

✅ Thank you! Your message has been sent successfully. We'll get back to you soon!
📧

Email

sanjeev.raila15@gmail.com

🏫

University

Mercer University

🔗

LinkedIn

sanjeev-raila