⚗️ DL Simulator — Dr. Essa Laboratory

A discrete-event queueing model simulator built for the Dr. Essa Diagnostic Laboratory. Models patient flow at the front desk during peak hours (9:00 AM – 11:00 AM) using analytical queueing theory formulas.

📸 Overview

The system allows users to configure queueing parameters and instantly compute key performance metrics such as average waiting time, queue length, server utilization, idle time, and lab throughput — for five queueing models with full multi-server support.

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🧮 Supported Models

Model	Arrival	Service	Multi-Server Support
M/M/s	Exponential	Exponential	✅ Exact (Erlang-C)
M/G/s	Exponential	General	✅ Cosmetatos Approximation
G/G/s	General	General	✅ Extended Kingman Approximation (Whitt)
M/M/1	Exponential	Exponential	(Single-server case of M/M/s)
M/G/1	Exponential	General	(Single-server case of M/G/s)
G/G/1	General	General	(Single-server case of G/G/s)

Supported General Distributions (G)

• Uniform — parameterized by Minimum and Maximum
• Normal — parameterized by Mean and Variance
• Gamma — parameterized by Mean and Variance

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📊 Performance Metrics Calculated

• λ — Arrival rate (patients/min)
• μ — Service rate (patients/min)
• ρ — Server utilization (per server)
• Idle Time — Fraction of time servers are idle
• Lq — Average number of patients waiting in queue
• L — Average number of patients in the system
• Wq — Average waiting time in queue (minutes)
• W — Average total time in system (minutes)
• Throughput — Expected patients served in 120 minutes
• Stability Status — Whether the system is stable (ρ < 1)

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⚙️ Prerequisites

Make sure you have the following installed on your system before running the project:

• .NET 8 SDK — required to build and run the backend API. Verify with dotnet --version.
• Node.js (v18 or higher) — required for the Next.js frontend
• npm (comes with Node.js)

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🚀 Getting Started

1. Clone the Repository

git clone https://github.com/developer-kamran/Diagnostic-Lab-Simulator.git
cd Diagnostic-Lab-Simulator

2. Run the Backend (ASP.NET Core API)

cd backend/DLSimulator.API
dotnet run

The API will start at http://localhost:5000. Swagger UI is available at http://localhost:5000/swagger.

3. Run the Frontend (Next.js)

Open a new terminal:

cd frontend
npm install
npm run dev

The frontend will start at http://localhost:3000.

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🔌 API Endpoint

POST /api/queue/calculate

Request Body Example (M/M/s — Multi-server):

{
  "modelType": 0, // 0 = M/M/s, 1 = M/G/s, 2 = G/G/s
  "arrivalDistribution": 0, // 0 = Exponential
  "arrivalMean": 5,
  "serviceDistribution": 0, // 0 = Exponential
  "serviceMean": 3,
  "numberOfServers": 3,
  "simulationDuration": 120
}

Request Body Example (G/G/s with Uniform distributions):

{
  "modelType": 2, // 0 = M/M/s, 1 = M/G/s, 2 = G/G/s
  "arrivalDistribution": 1, // 1 = Uniform, 2 = Normal, 3 = Gamma
  "arrivalMin": 2,
  "arrivalMax": 8,
  "serviceDistribution": 1, // 1 = Uniform, 2 = Normal, 3 = Gamma
  "serviceMean": 4,
  "serviceVariance": 2,
  "numberOfServers": 2,
  "simulationDuration": 120
}

Response:

{
  "modelType": 0, // 0 = M/M/s, 1 = M/G/s, 2 = G/G/s
  "numberOfServers": 1,
  "lambda": 0.2,
  "mu": 0.3333,
  "rho": 0.6,
  "idleTime": 0.4,
  "lq": 0.9,
  "l": 1.5,
  "wq": 4.5,
  "w": 7.5,
  "throughput": 24.0,
  "isStable": true,
  "stabilityMessage": null
}

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🛠️ Tech Stack

Layer	Technology
Backend	C# ASP.NET Core 8 Web API
Frontend	Next.js 14, Tailwind CSS

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📄 License

This project was developed for academic purposes as part of CSSE-607 — Modeling and Simulation.