Shadow Prices Vs. Vickrey Prices in Multipath Routing

Shadow price and Vickrey price are two classic metrics that can be applied to measure the relative importance of links in a communication network. Each metric has been extensively investigated and enjoys important applications. The authors study the underlying connections between these two metrics with seemingly different definitions, under a general mathematical model of multipath multi-session multicast routing. They show that Vickrey prices provide upper-bounds for shadow prices in general, and the fine granularity version of Vickrey price, unit Vickrey price, equals exactly the maximum shadow price.