Shockwave Theory.

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Presentation transcript:

Shockwave Theory

Definitions A shockwave describes the boundary between two traffic states that are characterized by different densities, speeds and/or flow rates. Shockwave theory describes the dynamics of shockwaves, in other words how the boundary between two traffic states moves in time and space. - Forward, - backward, - and stationary shock waves.

Shochwave Classifications

Shochwave Classifications

Shochwave Classifications Frontal stationary: head of a queue in case of stationary / temporary bottleneck. Forward forming: moving bottleneck (slow vehicle moving in direction of the flow given limited passing opportunities). Backward recovery: dissolving queue in case of stationary or temporary bottleneck (demand greater than supply); forming or dissolving queue for moving bottleneck.

Shochwave Classifications

Shochwave Classifications Forward recovery: removal of temporary bottleneck (e.g. clearance of incident, opening of bridge, signalized intersection). Backward forming: forming queue in case of stationary, temporary, or moving bottleneck* (demand greater than supply); Rear stationary: tail of queue in case recurrent congestion when demand is approximately equal to the supply.

Two traffic states: states 1 and 2 Two traffic states: states 1 and 2. Let S denote the wave that separates these states. The speed of this shockwave S can be computed by:

Graphical Interpretation of Shockwave Speed

Application of Shockwave Temporary over-saturation

Shockwaves at Bottleneck

Shockwaves Signalized Intersections

Flow into shockwave

Moving bottlenecks