implement off-ramp in METANET

[woodwm]

Hi,

I implemented off-ramp in METANET. Could you take a look at?

I think the condition (9) in the network valid check function needs to be removed.

sym-metanet/src/sym_metanet/network.py

Lines 500 to 506 in 2bedf26

	if any(self.out_links(node)):
	msgs.append(
	f"Expected node {node.name} to have no exiting links, as "
	f"it is connected to destination {destination.name}."
	)
	if raises:
	raise InvalidNetworkError(msgs[-1])

[FilippoAiraldi]

Hi @woodwm,

I took a look at your implementation of the off-ramp and pushed some new modifications to your pull request branch. Would you be so kind to take a look at them and see if they make sense to you as well?

In particular

• I reworked condition (9) of Network.is_valid: if a node has exiting links and a destination, this must be an off-ramp
• Node.get_downstream_density made sense to me, and I just refactored it to be a bit clearer
• I made heavier modifications for Node.get_upstream_speed_and_flow. Your implementation required all destinations to have a get_flow method. While I understand that it is correct, I think adding an assertion clarifies this requirement. Moreover, the DestinationEngine.get_offramp_flow method was a bit unnecessary in my opinion, as it achieves the same as the NodesEngine.get_upstream_flow. I also expanded the OffRamp.get_flow to support different scenarios
• I also added a new test and polished other small things, e.g., docstrings and missing implementations

[woodwm]

Hi, @FilippoAiraldi thank you a lot for your changes.

In the function Node.get_upstream_speed_and_flow, the node is the upper node of a link and can only be Offramp if it connects a destination. In a normal network, the assertion should not happen, but it is good to have it just in case something abnormal happens.

Recently I have been thinking about the density of the off-ramp. Not many papers describe in detail how to set the density of the off-ramp. I think it should not be the density of the last incoming segment, which is fine for a normal destination. In this case, the off-ramp flow is only a part of the incoming flow in that node, which means that the speed of the off-ramp is much less than that of the incoming link in the mainstream, even though the speed of the off-ramp is not used. This is strange to me.

I think the density of the off-ramp should be the density of first segment in the other exiting link. The following are from the METANET documantation. What do you think about this?

[FilippoAiraldi]

Hi @woodwm,

thanks for the answer, and good question on the density. I also agree that not many papers explain this point clearly (at least, the ones that I used as references), so I do not have a definite answer.

I sort of understand your suggestion, and I have some points to address.

• I have a counter-example that you may or may not agree with. Consider a very simple network with a single node, as below.

This node has one incoming link L_in, one exiting link L_out, and an off-ramp D. Suppose the turn-rate of the exiting link L_out is 0, and the turn-rate of the off-ramp D is 1, i.e., all the incoming vehicles from L_in are leaving the highway via the off-ramp D.

Now, intuitively speaking, I would expect the density of D to be equal to the density of L_in, and the density of L_out to be 0 (since no vehicle is turning into L_out). However, if we follow your reasoning, "the density of the off-ramp should be the density of first segment in the other exiting link", implying that the density of both D and L_out are 0.

Does this counter-example make sense, or am I overlooking something?

• equation A28 from your image describes the dynamics of the density of an out-link. I admit that this is something that I did not quite take into consideration when building the package, and I am not sure it would be easy to implement

• A minor thing, but how would you address the case of a node with an off-ramp and multiple exiting links?

[woodwm]

Hi, @FilippoAiraldi

I think your mentioned case is considered in the condition 3 as well. When the turn rate of $L_{out}$ is 0, it is the same as there is only one exit link and the density of the off-ramp should be the same as the last segment of $L{in}$, and the anticipation term in the link speed update equation is 0. This is the same as a normal destination node.

I think no need to implement equation A(28). The currently implemented downstream boundary conditions are good and enough.

I am also not sure how to set the density of off-ramp when there are multiple exit links except for the off-ramp. My current think is that the density of the off-ramp is used to calculate the virtual density in the case of multiple exit links (including the off-ramp). The idea is that the density of the off-ramp should not change significantly the virtual density.

$$\frac{\sum {\rho_{out}^2} + \rho_{off}^2 }{\sum{\rho_{out}} + \rho_{off} } = \frac{\sum {\rho_{out}^2} }{\sum{\rho_{out}} }$$

Then, we have
$$\rho_{off} = \frac{\sum {\rho_{out}^2}}{\sum{\rho_{out}}}$$

What do you think on this?

[FilippoAiraldi]

Hi @woodwm,

You are right, I did not pay enough attention to the third condition!

Regarding the case with one off-ramp and multiple exiting links, the only equation that came up in my mind is also the virtual downstream density $\rho_{off} = \frac{\sum {\rho_{out}^2}}{\sum{\rho_{out}}}$. It is unclear how one could otherwise compute it.

Other solutions that I can think of are

• we check in Network.is_valid that every node with an off-ramp has at most one exiting link, so that we don't have to address the issue of multiple exiting links
• similarly to congested destinations, we define the downstream density offered by an off-ramp as a user-defined value (in other words, an external disturbance signal affecting the system). At this point, it is up to the user whether to set this value high (emulating a congested off-ramp) or low (small anticipation term in the velocity update)