An urban district can move many vehicles when its streets are moderately occupied, yet become much less productive when queues spill through intersections. The macroscopic fundamental diagram summarizes that region-wide tension between traffic accumulation and completed movement.
The first act allows demand to rise on a grid until the interior becomes crowded. The next act meters vehicles entering the district, using current conditions to keep accumulation away from the most damaging range. Both runs use the same underlying demand and road network; the comparison asks whether admitting fewer vehicles now can let more trips finish over time. Highlighted perimeter signals show where the intervention acts, while the cumulative completion plot shows its system-level consequence. The insight is counterintuitive but operationally important: unrestricted entry can reduce a network's ability to serve traffic. A well-timed boundary control can protect that ability, even though some travelers wait outside.
How does congestion build up on a road, and what makes it disappear? Traffic conservation provides the most basic answer: vehicles cannot accumulate or vanish without crossing the boundaries of a road segment. If more vehicles enter than leave, the segment fills. If more leave than enter, it empties. When the two flows balance, the number of vehicles stays steady.
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Following every car is one way to simulate traffic, but large roads and networks often need a simpler description. The cell transmission model divides a road into short pieces and advances traffic in time steps, moving vehicles from one piece to the next only when upstream demand and downstream space allow it.
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How can a road carry less traffic even as more vehicles try to use it? Fundamental diagrams describe how the number of vehicles occupying a road relates to their average speed and to the rate at which traffic moves through it. When traffic is sparse, vehicles can travel quickly, but few are present. As the road fills, it initially carries more traffic. Beyond a critical level, vehicles interfere with one another and queues develop; adding still more vehicles can slow movement enough to reduce the flow.
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