Approximate analytical expressions for transportation network performance under demand uncertainty

Abstract

This paper deals with accounting for demand uncertainty in the symmetric traffic equilibrium problem. We initially show that by not accounting for long term demand uncertainty, the total network travel time obtained from the traffic equilibrium problem is substantially underestimated. Then, we develop closed form approximate analytical expressions for expected value and the variance of the network performance (a measure of total system travel time) resulting from uncertain demand. We empirically show the relationship between the uncertain OD demand and the link/path flows in a network with the assumption that the long term demand is normally distributed. Illustrative numerical experiments are conducted on multiple test networks and the total network impact in terms of total system travel time is compared with the derived analytical expressions. It is observed that the expressions for the expected value match very closely to the true system impact for small networks and becomes an approximation as the network size grows. The robustness (variance) expression is observed to be more deviant for larger networks than the expected value. However, the ordinal ranking of robustness was found to be consistent with the true network robustness. Further, recent work on OD correlations, applicability on large networks and directions for future research are discussed. The analytical expressions should allow the characterization of network uncertainty when link flow uncertainty is known.