Wednesday, November 28, 2012

Complex Systems and Networks


I have recently become very interested in complex systems. My question, which is not very hard to answer, is whether transportation networks and systems are complex? I would say yes, they are.

Following is a list of some of the reasons why a system might be considered to be complex, according to a recent paper, "Challenges in Complex Systems Science", published by Dirk Helbing and his colleagues:

  • Many heterogeneous interacting parts 
  • Interactions of autonomous agents

Transportation systems are complex because they consist of many heterogeneous interacting parts and agents. For example, a public transportation system in a city consists of bus routes, rail routes, park-and-ride facilities, and so on. Just imagine a Chicagoan commuter who lives in a suburb. Every morning she drives her car, picks up a colleague on her way to a Metra station (carpooling), parks her car in a designated park-and-ride facility and both ride Metra to downtown. Then from the Metra station in downtown, they transfer to a bus to get to their office. Throughout this commute trip, different heterogeneous parts and agents are indeed interacting. As another example, bus bunching (also train bunching) is a direct result of uncoordinated interactions between different agents (buses or trains) in a public transportation system.

Other characteristics of complex systems are:
  • Path-dependent dynamics
  • Complicated transition laws
  • Self-organization or collective shifts
  • Non-equilibrium dynamics
  • Adaptivity to changing environments
  • Multilevel dynamics and so on.

Some of my recent findings on network traffic science suggest that network traffic dynamics are path-dependent. In fact, in a paper published in TRR in 2012, "Exploring Properties of Network-wide Flow-Density Relations in a Freeway Network", we suggested a path-dependent characterization of hysteresis in network traffic. Hysteretic transitions in traffic, either in macro scale on a single facility or in network scale, can be considered as complicated transitions laws. Self-organizing behavior of pedestrian crowds and the existence of the Network Fundamental Diagram (NFD) of road networks, as a collective effect of interacting vehicles in a network, are another examples.

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