By Jacob R. Mecklenborg
What of these ghostly catacombs that lie dormant under urban streets? these subway tunnels, by no means complete, by no means choked with the screeches of trains and the busy commotion of commuters. simply there. lifeless. You've heard of the subway's dying. The tunnels have been too slender. town used to be too broke. A grand miscalculation. good, so much of what you've heard is, sorry to claim, unfaithful. the preferred tale of the subway's loss of life is myth-laden and as incomplete because the unique plan. the total tale, lengthy buried in mounds of public files dispersed within the city's libraries, is now published. neighborhood writer Jacob Mecklenborg emerges from these dusty tomes with a clean, thought-provoking, complete exam of the subway's loss of life and what its destiny may possibly carry.
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Extra info for Cincinnati's Incomplete Subway: The Complete History (OH)
After imposition of the newly determined link tolls tj,**1', as A, a subset of revealed link flows vj*+1), a s. A are observed. The observed link flows are the result of distribution of the realized O-D demands on the network, and thus provide useful information about the true but unknown demand functions. Thus we can use the BLPP technique to estimate or update the O-D matrix and the approximate demand functions from the newly available link traffic counts, thereby obtaining anew set ofupdated O-D demand functions gw(cw,6(*+1> j , we W .
Convergence pattern of the sequential trial-and-error toll adjustment scheme for the second-best pricing problem in Example 2 Sequential experimental approach for analyzing second-best road pricing 39 Figure 5. Convergence pattern of the sequential linear demand function approximation in Example 2 Figure 5 displays the successive linear approximation to the true, but unknown, nonlinear demand functions. It is observed that, as the trial experiment continues, the linear approximation does become more tangential to the true demand curve near the true optimum points on the demand curve.
If every link is subjected to a nonnegative toll charge, then one immediate solution to the above BLPP is to use link tolls that are based on marginal-cost pricing and are given as (Yang and Huang, 1998): dt (v ) 1a=Va^TJLL > a e A (6) dv0 where v* = (v*,a e A\ and d" =(d"w,we W\ are the system-optimal solution that solves max V fg~'(co)dco-Y;„(¥„)v (7) In the iterative procedure developed by Yang et al. (2004) for marginal-cost pricing in the absence of demand functions, link tolls are adjusted with the change in observed link flows or according to the explicit formula (6) using the convergent method of successive averages.