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Scale-Free Phenomena in Communication Networks: A Cross-Atlantic Comparison

  • Communication
  • Design
  • Mathematics


?Small-world networks? have a high degree of local clustering or cliqueness, like a regular lattice and a relatively short average minimum path, like a completely random network. The huge appeal of ?small-world networks? lies in the impact they are said to have on dynamical systems. In a transportation network, ?small-world? topology could improve the flow of people or goods through the network, which has important implications for the design of such networks. Preliminary research has shown that ?small-world network? phenomenon can arise in traffic networks possessing ?small-world? network topology (i.e., in a network that has a structure somewhere in between a regular lattice and random graph) and that, at least under certain circumstances, traffic appears to flow more efficiently through a network with such topology (Schintler and Kulkarni, 2000). This paper will explore this further through simulation under varying assumptions regarding the size of the network (i.e., in terms of number of nodes and edges), the level of traffic in the network, the uniformity of nodes and edges and the information levels of travelers in the network. The simulations will be done using the random rewiring process introduced by Watts and Strogatz (1998), where each time the network is rewired, the distribution of traffic and congestion through the network, and the ?small-world? network parameters, shortest average minimum path and clustering coefficient, will be examined. Traffic flow will be estimated using a gravity model framework and a route choice optimization program. The simulations will also be used to reveal whether or not there are certain nodes or links that suffer at the expense of the entire network becoming more efficient. In addition, the possibility of a self-organised criticality (SOC) structure will be examined. The concept, introduced by Bak et al.,(1987), gained a great deal of attention in past decades for its capability to explore the significant and structural transformation of a dynamic system. SOC sets out how prominent exogenous forces together with strong localized interactions at the micro level lead a system to a critical state at the macro-level. A further step in our analysis is the investigation of whether a power-law distribution, characteristic of the SOC state, evolves in the traffic network. While ?small-world? network topology may be shown to improve the efficiency of traffic flow through a network, it should be recognized that ?small-world? networks are sparse by nature. The shut down or major disruption of any link in such a network, particularly one with heavy congestion, could provoke significant disorder. This paper will also explore the effect that disruptions of this nature have on networks designed with a high degree of local clustering and a short average minimum path. The fact that a ?small-world? network is sparse also raises other issues for the transportation planner. If ?small-world? topology is in fact a desirable property for transportation networks, how do we transform existing networks to produce these results? Unlike other networks, such as those for telecommunications or socialization, a transportation network cannot be rewired to achieve a more efficient network structure. This issue will also be addressed in the paper. REFERENCES Bak, P., C. Tang, and K. Wiesenfeld (1987), ?Self-Organised Criticality?, Physical Review Letters, Vol. 59 (4), pp. 381-384. Watts, D.J. and S.H. Strogatz (1998). ?Collective Dynamics of ?Small-World? Networks? Nature, Vol 393, 4, pp. 440-442. Schintler, L.A. and R. Kulkarni (2000). ?The Emergence of Small-World Phenonmenon in Urban Transportation Networks? in Reggiani, A. (ed.), Spatial Economic Science: New Frontiers in Theory and Methodology, Springer-Verlag, Berlin-NewYork, pp. 419-434.

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