Locations of Medians on Stochastic Networks

Abstract

The definition of network medians is extended to the case where travel times on network links are random variables with known discrete probability distributions. Under a particular set of assumptions, it is shown that the well-known theorems of HAKIMI and of LEVY can be extended to such stochastic networks. The concepts are further extended to the case of stochastic oriented networks. A particular set of applications as well as formulations of the problem for solution using mathematical programming techniques are also discussed briefly.