Waves, queues, bottlenecks, and the laws behind moving traffic.
A disturbance becomes a wave
Not every traffic jam begins at a crash, lane closure, or visible road defect. On a busy road, one driver's brief slowdown can force the next driver to brake a little more, and that reaction can repeat from car to car. A self-sustaining queue may then appear without a permanent obstacle.
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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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Traffic can behave differently on the way into congestion than on the way out. Even if travel demand returns to an earlier level, queues and unevenly loaded roads may remain. The present state depends partly on the path taken to reach it.
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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.
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A slow vehicle can reduce the usable capacity of a road even though the vehicle itself keeps moving. Cars catch it, bunch behind it, and create a disturbance that travels back through the traffic stream. The location of the obstruction and the location of its resulting congestion need not remain together.
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A vehicle platoon can look orderly until the lead car makes a small speed change. The important question is what happens farther back: does each follower smooth the disturbance, or does each reaction make it larger? String stability names the condition in which the disturbance does not amplify as it moves through the line.
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When an entrance and exit ramp sit close together, arriving vehicles need to merge while others need to leave. These crossing intentions turn a short road section into a weaving area, where frequent lane changes can disrupt through traffic and send congestion upstream.
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