Statistics for a Random Network Design Problem

We investigate a random network design problem speci…ed by a complete graph with n nodes whose edges have associated …xed costs that are independent random variables, and variable costs associated that are also independent random variables. The objective is to …nd a spanning tree whose total …xed cost plus total variable cost is minimum, where the total variable cost is the sum of variable costs along all paths from a source node to every other node. Here we examine the distributions of total …xed cost and total variable cost obtained from random tree generation, and compare the expectations in solving the di¤erent components of a random network design problem using simulation.