Abstract
Dial [Transportation Research B 33 (1999) 189] derived a fast algorithm for computing Minimal-Revenue (MR) congestion pricing (tolls) in single-origin, multiple destination networks, with fixed demands. This pricing induces the same system optimized network flow as Marginal Cost congestion pricing (tolls). Dial reported “Bad News”: the algorithm works for multiple destinations, but only one origin. We show some “Good News”: the algorithm works also for multiple origins and a single destination. Dial reported “Good News”: “MR tolls often remain constant even as trip demand changes”. We show more “Good News”; two general conditions sufficient to cause piecewise constant MR tolls. Dial reported “No News”: that the MR pricing supports elastic demand as well as fixed demand. We show here some “Bad News”: when demands are elastic, MR pricing does not accomplish its purpose of replicating the system optimal flows generated by Marginal Cost (MC) congestion pricing. We provide numerical examples with tabular and graphical solutions to illustrate this failure of MR tolls.
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