Equilibrium condition-based optimization models for network-wide travel time estimation using limited observed data

This paper presents a series of optimisation models to estimate network-wide travel times under equilibrium conditions. The proposed models estimate the upper and lower bounds (ULB) of the maximum total travel time (MTTT), path travel time (PTT), and link travel time (LTT). The uncertainty range of travel time is obtained by subtracting the upper bound of travel time from the corresponding lower bound. To minimise the uncertainty ranges of the estimated travel times, the relationship of PTTs is introduced as a generalised equilibrium condition. Numerical experiments show that adopting the equilibrium condition can minimise the uncertainty ranges of the travel time estimation. The proposed method can also more accurately estimate the travel times even when the observed data are limited in the entire network. These findings provide a basis for further research on the travel time observability problem of travel time estimation for the whole territory of the network.