Mathematical Modelling of Traffic Flow at Bottlenecks

This master’s thesis gives a brief overview of mathematical modelling of traffic flow from different perspectives. Focus lies on the fluid flow analogy first derived by Lighthill, Whitham and Richards (LWR) in the 1950’s which treats a traffic stream as a compressible one-dimensional fluid. The LWR theory is applied to bottleneck queueing situations, more specifically to junctions with one outgoing and two incoming roads. Problems are analysed through two different models, utilising two different sets of flow merge rules. The models are compared and contrasted through steady-state solutions and more general queueing situations. Benefits and drawbacks of the respective models are discussed and some further modifications and extensions are suggested.