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As it happens, I studied traffic flow back when I was an undergrad in the context of "agent based modeling". Agent-based models are basically computer simulati

As it happens, I studied traffic flow back when I was an undergrad in the context of "agent based modeling". Agent-based models are basically computer simulations where you throw N 'agents' into an environment with pre-defined rules and then watch how they interact with each other. This setup lends itself perfectly to vehicle-flow; each agent is a car, each car has a model for when it accelerates, when it slows down, when it turns, and so forth. Create enough of them, and you can start to simulate traffic jams and other interesting traffic phenomena. Now, I have not studied this problem in particular. My research was on the effect of excessive lane-changing on overall traffic throughput (Spoiler: lane-changing tends to cause traffic to slow down behind the lane-changer, which means that system-wide lane-changing leads to traffic jams, but changing lanes is a strictly superior strategy for individual drivers in most situations. The classic collective-action problem. Economics!) However, it seems to me that it would be relatively simple to extend a traditional AB traffic model to include special vehicles that impose constraints on nearby cars. If any of you are interested, there is an excellent java library developed at UChicago called Repast [http://repast.sourceforge.net/index.html http://repast.sourceforge.net/index.html] which contains a framework for building agent-based models. You may also be interested in my favorite book on the subject, "Micromotives and Macrobehavior" [http://www.amazon.com/Micromotives-Macrobehavior-Lectures-Public-Analysis/dp/0393090094 http://www.amazon.com/Micromotives-Macrobehavior-Lectures-Pu...] which is more rigorous than its Amazon description would have you believe.

yummyfajitas 15y ago
I don't think you need agent models. You can probably study this directly with the nonlinear transport equation (Lighthill-Witham, I think), or one of the more detailed versions (the Rascall model?). All you need to do is impose a police-created boundary condition at x=cop_location(t) instead of solving the pde on free space: velocity(density)|x=cop_location(t) = cop_velocity(t).
- politician 15y ago
  Would that model take into account the number of lanes and the lane position of the cop?
  - yummyfajitas 15y ago
    It's been a while since I looked, so I'd need to think carefully. But very likely, yes, you could incorporate such things. What I'd do is in the speed control term V(1-u(x,t)), I'd probably make V vary w.r.t the distance to the cop. I.e., same lane, you'd take something like: [V+(V_cop-V)bump(x-cop_position)](1-u(x,t)) Whereas in different lanes, you'd take: [V+alpha(V_cop-V)bump(x-cop_position)](1-u(x,t)) where alpha < 1 measures the reduced effect the cop has on different lanes. (Alpha might vary from lane to lane if you have more than 2 lanes, i.e. if the cop is in lane 1, alpha_lane_5 might be much smaller than alpha_lane_1.) Here, bump(z) is some sort of bump function - 1 near z=0, dropping off as z moves away.

yummyfajitas 15y ago

I don't think you need agent models. You can probably study this directly with the nonlinear transport equation (Lighthill-Witham, I think), or one of the more detailed versions (the Rascall model?). All you need to do is impose a police-created boundary condition at x=cop_location(t) instead of solving the pde on free space: velocity(density)|x=cop_location(t) = cop_velocity(t).

politician 15y ago
Would that model take into account the number of lanes and the lane position of the cop?
- yummyfajitas 15y ago
  It's been a while since I looked, so I'd need to think carefully. But very likely, yes, you could incorporate such things. What I'd do is in the speed control term V(1-u(x,t)), I'd probably make V vary w.r.t the distance to the cop. I.e., same lane, you'd take something like: [V+(V_cop-V)bump(x-cop_position)](1-u(x,t)) Whereas in different lanes, you'd take: [V+alpha(V_cop-V)bump(x-cop_position)](1-u(x,t)) where alpha < 1 measures the reduced effect the cop has on different lanes. (Alpha might vary from lane to lane if you have more than 2 lanes, i.e. if the cop is in lane 1, alpha_lane_5 might be much smaller than alpha_lane_1.) Here, bump(z) is some sort of bump function - 1 near z=0, dropping off as z moves away.