Application of shadow price in capacity expansion of state dependent routing

We develop a capacity expansion method for state dependent routing which utilizes the concept of shadow price. To cope with the computational complexity which is inherent with the capacity expansion process, special forms of fixed point iteration are developed for network blocking evaluation. The proposed capacity expansion method is illustrated through the example of a well known state dependent routing, namely Least Busy Alternate Routing. We verify the method in simulated networks and the resulting network cost is seen to be quite close to the ones derived from the methods with much higher computational complexity. The proposed method also results in a network design that satisfies the prescribed network blocking probability very accurately.