Posted by Rick Denney on February 22, 2004 at 18:54:53:
In Reply to: Re: Re: Re: Re: Wow for the Lipton/Veronie Recital!!! posted by jeff m on February 22, 2004 at 17:30:47:
Warning! Jeff didn't leave an email addres, or I'd have sent this directly. No Tuba Content!
There are two modeling approaches, microscopic and macroscopic, and the former doesn't use a continuous fluid model at all. The microscopic approach models traffic as kinematic particles, each with its own rules, rather than as a fluid. As they move, the simulation keeps track of their behavior and sums it up into general performance measures, such as delay, stops, average speed, and so on. Most traffic simulations take the microscopic approach, with stochastic mechanisms for describing vehicles-driver units and their trip patterns. Examples include CORSIM, VISSIM, Paramics, AIMSUN, and others.
And then there are models that are based on cellular automata, where the network is divided into fixed segments so small that only one thing can happen in them during any arbitrarily short time step, and they pass cars from segment to segement. This is also microscope, but it keeps track of the road rather than the car. The example is TransSims.
There have been various attempts to model traffic as a fluid, but most have so many flaws that they aren't that useful. One example is the Hydrodynamic Model, which was popular to think about in the 30's and up through the late 60's, when computers made microscopic modeling possible. They only still exist as historical approaches. The one exception is a macroscopic modeling approach that describes traffic as two fluids. It relates the total travel time per trip to stopped time per trip, with trips being defined either as a constant distance or a constant travel time. It draws a curve that relates the total trip time to the stopped time, which is a characteristic curve for each network that works in all demand conditions. This approach is called the Two-Fluid Model, and it is so easy it can be done with general statistics software. The two fluids are cars running, which is compressible (density is less than jam density), and cars stopped, which is uncompressible (at jam density).
(You've just gotten a glimpse of the sorts of things I do for a living.)
Rick "since you asked" Denney