Dashboard 00:00:00
LIVE MONITORING
⚠️ CONGESTION ALERT: Heavy traffic detected at NH-48 Delhi-Gurgaon Expressway
Active Intersections
🚦
156
▲ 12 new today
Vehicles Tracked
🚗
24,831
▲ 8.3% vs yesterday
Avg Speed (km/h)
⚡
34.7
▼ 2.1 km/h
Congestion Points
🔴
18
▲ 3 new alerts
Optimization Score
📊
87%
▲ 4.2% improved
Avg Wait Time
⏱️
42s
▼ 8s reduction
📈 Traffic Flow - 24 Hours Real-time
🏙️ City-wise Traffic Load Top 8 Cities
📋 System Activity Log
🎯 Quick Actions
🗺️ India Live Traffic Map
📍 Map Legend
Free Flow (0-30%)
Light (30-50%)
Moderate (50-70%)
Heavy (70-85%)
Severe (85-100%)
Monitored Junction
Active Route
📊 Selected City Info

Select a city on the map

City--
Density--
Avg Speed--
Active Signals--
Vehicles/hr--
Congestion Level--
CONGESTION METER
🔴 Active Alerts
🔢 Origin-Destination Traffic Flow Matrix

This O-D matrix represents traffic flow volumes (vehicles/hour) between major Indian city junctions. Colors indicate density levels. The matrix is used for signal timing optimization.

📊 Flow Distribution
🔍 Matrix Properties
Matrix Dimension10 × 10
Total Flow Volume--
Max Single Flow--
Min Non-Zero Flow--
Average Flow--
Eigenvalue (λ₁)--
Matrix Rank--
Sparsity--
Symmetry Index--

INTELLIGENT SIGNAL CONTROL SYSTEM

Matrix-optimized adaptive signal timing for Indian intersections

📊 Hourly Vehicle Count
🥧 Vehicle Type Distribution
📈 Weekly Congestion Trend
⚡ Speed vs Density Analysis
📉 Before vs After Optimization Comparison
🧮 Matrix-Based Traffic Flow Algorithm
1 Data Collection & Matrix Formation
Collect real-time traffic data from sensors at each intersection. Form the Origin-Destination (O-D) matrix M[n×n] where M[i][j] represents traffic flow from intersection i to intersection j.
2 Traffic Density Computation
Calculate density vector D = M × 1ₙ (row sums) for outgoing flow and D' = Mᵀ × 1ₙ (column sums) for incoming flow. Total density at node i: ρᵢ = Dᵢ + D'ᵢ
3 Eigenvalue Analysis
Compute eigenvalues of the normalized flow matrix to identify dominant traffic patterns and critical flow directions. The principal eigenvalue λ₁ indicates overall network load.
4 Signal Timing Optimization
Apply Webster's formula with matrix corrections: Cₒ = (1.5L + 5)/(1 - Σyᵢ) where yᵢ = qᵢ/sᵢ is the flow ratio from the matrix analysis. Green time: gᵢ = (yᵢ/Σyᵢ) × (Cₒ - L)
5 Iterative Convergence
Iterate the matrix transformation M' = P × M × Q where P and Q are optimization matrices until convergence (|M'−M| < ε). This redistributes flow for minimum total delay.
6 Adaptive Feedback Loop
Continuously update the matrix with new sensor data every 30 seconds. Apply Kalman filtering for prediction: M̂(t+1) = A × M(t) + K × (Z(t) − H × M(t))
💻 Core Algorithm (Pseudocode)
// Matrix Traffic Flow Optimization function optimizeTrafficFlow(matrix M, threshold ε): // Step 1: Compute density vectors D_out = M × 1_n // Row sums D_in = Mᵀ × 1_n // Column sums ρ = D_out + D_in // Total density // Step 2: Normalize flow matrix N = M / max(M) // Step 3: Eigenvalue decomposition [λ, V] = eigen(N) λ₁ = max(λ) // Dominant eigenvalue // Step 4: Iterative optimization while (convergence > ε): P = computeOptMatrix(ρ, λ) M_new = P × M × Pᵀ // Webster's signal timing for each intersection i: y_i = ρ[i] / capacity[i] C_opt = (1.5*L + 5)/(1 - Σy) g[i] = (y_i/Σy) × (C_opt - L) convergence = ||M_new - M|| M = M_new return {signals: g, matrix: M}
📐 Mathematical Model

Traffic Flow Matrix:

M = [mij]n×n, where mij = flow from i → j

Density Vector:

ρi = Σⱼ mij + Σⱼ mji

Optimization Objective:

min Σᵢ di(gi, ρi)
s.t. Σ gi = C - L, gi ≥ gmin

Webster's Delay Formula:

d = C(1-λ)²/2(1-λx) + x²/2q(1-x)

Greenshields Model:

v = vf(1 - k/kj)

Matrix Based Traffic Flow Control System

An intelligent traffic management solution leveraging matrix mathematics, real-time data analysis, and adaptive signal control to optimize traffic flow across Indian cities. Built with modern web technologies for real-time monitoring and control.


🗺️

Real-time Map Analysis

Live traffic monitoring on Indian map with density heatmaps, route tracking, and congestion alerts using OpenStreetMap.

🔢

Matrix Computation

O-D traffic flow matrix with eigenvalue analysis, density computation, and optimization using linear algebra techniques.

🚦

Adaptive Signals

Webster's formula-based signal timing with real-time adjustments driven by matrix-computed traffic density vectors.

📊

Advanced Analytics

Comprehensive analytics with speed-density analysis, hourly trends, vehicle classification, and before/after comparisons.

🤖

Auto Optimization

Iterative convergence algorithm that automatically optimizes signal timings to minimize total network delay.

🚨

Emergency Control

Priority-based emergency vehicle routing with instant signal override and corridor clearance capabilities.

🛠️ Technology Stack

Frontend

HTML5 / CSS3✓
JavaScript ES6+✓
Leaflet.js Maps✓
Chart.js✓

Algorithms

Matrix Algebra✓
Webster's Formula✓
Greenshields Model✓
Eigenvalue Analysis✓

Data

OpenStreetMap✓
Simulated Sensors✓
Real-time Updates✓
Indian City Data✓
👥 Project Team
S

Student Name

Lead Developer

G

Guide Name

Project Guide

D

Department

Computer Science & Engg

C

College Name

Your University