Cellular Automaton Modeling of Passenger Transport Systems
Akiyasu Tomoeda · InTech eBooks · 2012
Jamming phenomena are observed everywhere in our daily live.These stagnations in flow occur not only on highways, but also in stadiums, in public transportation like buses and trains, in the world of the Internet, and even in our bodies.Almost everyone will have a negative image of a "jam", which means the clogging of the flow of traffic, however we do have positive reactions to some kinds of jams.For instance, it is gratifying to interrupt the transmission of infectious disease or prevent the spreading of fire.The important point is that all these kinds of phenomena have the commonality of being a congestion in a transporting process which comes about through a universal jamming formation process.Especially from the point of statistical physics, these jamming phenomena are also interesting as a system of interacting particles, such as vehicles, pedestrians, ants, Internet packets, and so on, driven far from equilibrium.By considering all the above particles in various transporting processes as "Self-Driven Particles" (SDPs), we are allowed to treat various transportation phenomena universally under the physics of complex systems [1][2][3] .This interdisciplinary research on jamming phenomena of SDPs in various fields has been recently termed as "Jamology" [4,5] .Now, let us consider the state of "Jam", i.e., what is a "Jamming flow"?It is difficult for anyone to answer this question exactly.Japanese expressway companies incorporate specific threshold velocities to define the jamming flow.That is, if the average traffic velocity becomes less than the defined threshold velocity, the state of traffic is considered to have transitioned to a jamming flow.Whereas, if the average traffic velocity is above the threshold, the state of traffic flow corresponds to "Free flow".For example, one company defines the threshold velocity to be 40km per hour.In this case, if the average traffic velocity becomes less than 40km per hour, the state of traffic flow is called jamming flow.Whereas, another company identifies jamming flow by defining the threshold as 30km per hour.There is a lack of uniformity, since the definition of jamming flow depends on the company.Moreover, when it comes to considering the jamming phenomena in the dynamics of non-vehicles, such as pedestrians and ants, it becomes difficult to properly translate these definitions based on threshold velocity to another definition of the jamming state in the dynamics of non-vehicles.Thus, we should begin to provide a clear definition of jamming flow in the next section to study jamming phenomena as a mathematical science.