Reliability-based user equilibrium in a transport network under the effects of speed limits and supply uncertainty

Abstract

This study investigates the system-wide traffic flow re-allocation effect of speed limits in uncertain environments. Previous studies have only considered link capacity degradation, which is only one of the factors that lead to supply uncertainty. This study examines how imposing speed limits reallocates the traffic flows in a situation of general supply uncertainty with risk-averse travelers. The effects of imposing a link-specific speed limit on link driving speed and travel time are analyzed, given the link travel time distribution before imposing the speed limit. The expected travel time and travel time standard deviation of a link with a speed limit are derived from the link travel time distribution and are both continuous, monotone, and convex functions in terms of link flow. A distribution-free, reliability-based user equilibrium with speed limits is established, in which travelers are assumed to choose routes that minimize their own travel time budget. A variational inequality formulation for the equilibrium problem is proposed and the solution properties are provided. In this study, the inefficiency of a reliability-based user equilibrium flow pattern with speed limits is defined and found to be bounded above when supply uncertainty refers to capacity degradation. The upper bound depends on the level of risk aversion of travelers, a ratio related to the design and worst-case link capacities, and the highest power of all link performance functions.