Reliable network design under supply uncertainty with probabilistic guarantees

Abstract

This paper proposes a bi-level risk-averse network design model for transportation networks with heterogeneous link travel time distributions. The objective of the network design is to minimise the total system travel time (TSTT) budget (TSTTB), which consists of the mean TSTT and a safety margin. The design is achieved by selecting optimal link capacity expansions subject to a fixed expansion budget. Users’ selfish behaviour and risk attitude are captured in the lower level traffic assignment constraints, in which travellers select routes to minimise their own path travel time budget. The properties of the design problem are analysed analytically and numerically. The analysis shows that despite the lack of knowledge of travel time distributions, the probabilities that the actual TSTT and the actual path travel time are, respectively, within the optimal TSTTB and the minimum path travel time budget under optimal design have lower bounds. The lower bounds are related to the system manager's and travellers’ risk aversion. The optimal TSTTB is proven to be bounded below even when the link expansion budget is unlimited.