I want to apply the shockwave theory to the traffic behaviour at weaving section with an auxiliary lane. What is the appropriate methodology? Is it appropriate to apply the theory of moving bottleneck for such a case? Also is it better to analyse traffic density per lane for the application of shockwave theory given that the weaving section and the upstream traffic has unequal number of lanes?
in your problem you are saying ''weaving section with an auxiliary lane'' and upstream with unequal number of lane. i think its most of kind of stationary bottleneck, with can generate different type of traffic shock waves.
You may need to watch this lecture:
https://ocw.tudelft.nl/course-lectures/5-moving-bottleneck-queuing-s-p-hoogendoorn/
You can use Carlos F. Daganzo's Variational theory, which incorporates
shockwave speed to calculate the microscopic traffic state ( vehicle trajectory ).
You can see this publication too : Article Variational formulation incorporating spatial capacity chang...
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