Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand

Network pricing serves as an instrument for congestion management, however, agencies and planners often encounter problems of estimating appropriate toll prices. Tolls are commonly estimated for a single-point deterministic travel demand, which may lead to imperfect policy decisions due to inherent uncertainties in future travel demand. Previous research has addressed the issue of demand uncertainty in the pricing context, but the elastic nature of demand along with its uncertainty has not been explicitly considered. Similarly, interactions between elasticity and uncertainty of demand have not been characterized. This study addresses these gaps and proposes a framework to estimate nearest optimal first-best tolls under long-term stochasticity in elastic demand. We show first that the optimal tolls under the deterministic-elastic and stochastic-elastic demand cases coincide when cost and demand functions are linear, and the set of equilibrium paths is constant. These assumptions are restrictive, so three larger networks are considered numerically, and the subsequent pricing decisions are assessed. The results of the numerical experiments suggest that in many cases, optimal pricing decisions under the combined stochastic-elastic demand scenario resemble those when demand is known exactly. The applications in this study thus suggest that inclusion of demand elasticity offsets the need of considering future demand uncertainties for first-best congestion pricing frameworks.