SMART TRAFFIC SIGNAL OPTIMIZATION

LIVE STATUS

Current Phase
-
Signal Countdown
-s
Queue Length
0
Cars Passed
0
Green Roads
-
Red Roads
-

PERFORMANCE

-
Efficiency Score
0%
Throughput
0
Average Waiting Time
0s

LIVE TRENDS

Queue Throughput

SIMULATION MODE

Mode: Normal Traffic
Mode Intensity Medium
Scenario Presets
Pick a preset to simulate a real-world traffic pattern.

ROAD-WISE TRAFFIC

TRAFFIC CONTROLS

Emergency Priority
No priority active
Manual Density

GRAPH MODEL

Phases: -
Conflict edges: -
Current phase explanation: -

ABOUT & GUIDE

1. Quick Start
Use this flow for a complete run:
  • Press START to begin traffic movement and signal rotation.
  • Press STOP to pause while preserving current state.
  • Press RESET to clear traffic and restart from a clean state.
2. Simulation Modes
  • Normal Traffic: stable everyday pattern with moderate load.
  • Balanced Traffic: similar demand on all four roads.
  • Heavy Traffic: high inflow and longer queues.
  • Random Traffic: continuously varying demand.
Mode Intensity summarizes expected pressure level.
3. Scenario Presets
  • Peak Hour: office-time surge with strong directional demand.
  • School Exit: short controlled burst around one time window.
  • Event Dispersal: one random road gets higher focus each run while others continue moving with lower load.
Presets automatically apply a mode and road-wise density profile.
4. Traffic Controls
  • Emergency Priority: temporarily prioritizes one road when urgent flow is needed.
  • Manual Density +/-: increase or decrease incoming demand per road in real time.
5. Live Status Metrics
  • Current Phase: active signal phase selected by graph-coloring logic.
  • Signal Countdown: remaining time before next phase switch.
  • Queue Length: total waiting vehicles across roads.
  • Cars Passed: cumulative successful crossings.
  • Green Roads / Red Roads: currently allowed and blocked directions.
6. Performance Metrics
  • Efficiency Rating: qualitative result from system throughput behavior.
  • Efficiency Score: numeric score for easier comparison.
  • Throughput: vehicles passing per minute.
  • Average Waiting Time: average delay before movement starts.
  • Live Trends: queue and throughput history over time.
7. Road-wise Traffic Card
  • Shows per-road Queue, Density, and current signal color state.
  • Useful for verifying if manual controls and scenarios are behaving correctly.
8. Graph Model (Discrete Maths Core)
  • Each direction (North, South, East, West) is treated as a vertex.
  • Unsafe simultaneous pairs are modeled as conflict edges.
  • Graph coloring groups non-conflicting vertices into safe phases.
  • The active colored group is turned green together to avoid collisions.
9. Applications of Discrete Mathematics Used
  • Set Representation: roads, cars, active roads, inactive roads, and conflict pairs are modeled as finite sets.
  • Set Partitioning: each signal phase partitions directions into two disjoint sets: green (allowed) and red (blocked).
  • Binary Relations: conflict relation defines which two roads cannot be green together at the same time.
  • Graph Theory: the junction is represented as a graph where roads are vertices and conflicts are edges.
  • Subgraph Reasoning: currently active roads form a conflict-free subset (independent set behavior).
  • Graph Coloring: colors represent safe phases; roads with the same color can move simultaneously.
  • Chromatic Insight: minimum required phase groups are derived from graph conflicts.
  • Functions and Mapping: mode/scenario selection maps to density values and spawn configurations.
  • Function Composition: scenario + mode + manual density updates combine to produce final traffic behavior.
  • Finite State Machine: the controller transitions through phase states with deterministic timing rules.
  • Discrete Time Steps: simulation updates in fixed ticks, making movement and decisions discrete.
  • Propositional Logic: if-then rule checks drive decisions (priority, conflicts, waiting, switching).
  • Constraint Satisfaction: safety constraints prevent invalid signal combinations that could cause collisions.
  • Combinatorics (Counting): queue length, cars passed, and road-wise waiting counts are discrete cardinalities.
  • Discrete Optimization: throughput maximization and waiting-time reduction guide signal effectiveness.
  • Weighted Random Choice: probabilistic spawning uses density-based weights to model realistic arrivals.
  • Case-Based Discrete Modeling: Peak Hour, School Exit, and Event Dispersal encode real situations as finite rule sets.