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Uncoordinated agents in society usually assumed to take their own optimal strategies do not always achieve the social optimum. In transportation network, travelers are assumed to choose the route that minimizes their own travel costs, which will form a Nash Equilibrium called user equilibrium where no one could be better off by changing routes in the network. This type of routing strategy named self-routing is socially suboptimal. Consequently the society has to pay a price of anarchy for the lack of coordination among travelers. In this paper we revisit the definition of price of anarchy (POA) and analyze its upper bound under different latency functions. We review some simulation results of several major cities and investigate the difference between optimum and actual system performance in the real transportation network. A numerical simulation of Sioux network is conducted based on the classical computational procedures. The results indicate that the shape of POA as a function of input flow is not diatonic but rather fluctuating. Then we propose some more insights of POA.