THE EQUILIBRIUM WORTH OF A NETWORK LINK

An arbitrary link (T) on a directed network whose link costs are fixed, unknown, differentiable disutility functions of link flows (with a symmetric Jacobian) is selected. Graded variations are induced in the "intrinsic" cost of T due to its own flow by varying the coefficient vector of a control polynomial of this flow. Sensitivity analysis of such perturbations on the unevaluated equilibrium cost (C) for any origin/destination (O/D) pair with arbitrary demand focuses on the marginal contribution to C of T's equilibrium flow (U sub T). This "shadow price" of U sub T, as well as the gradient components of C relative to the coefficient vector, are all positive multiples; and they can all be determined from output-data obtained locally at T. For affine link costs, the shadow price of U sub T remains constant on every utilized (sub)network as the coefficient vector and O/D-demand both vary, and T-local data then yields a polygonal map with which to predict the resulting link utilization patterns and the variations of C at large.

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  • Accession Number: 00485540
  • Record Type: Publication
  • Files: TRIS, ATRI
  • Created Date: Jul 31 1989 12:00AM