Robust Tolling Schemes for High-Occupancy/Toll (HOT) Facilities Under Variable Demand

High-Occupancy/Toll (HOT) lanes have become an increasingly prevalent form of congestion management pricing in the U.S. over the past few decades. The success of a HOT facility is dependent on the pricing scheme implemented, which determines the utilization of the HOT lane, and the corresponding congestion relief on the parallel general-purpose (GP) lanes. An additional complexity in determining HOT tolls arises from the inevitable variability in travel demand, which is inherent to transport networks. A successful tolling scheme, whether fixed or time-varying, must therefore be robust to changes in travel demand. In this paper we examine various tolling schemes for HOT facilities in efforts to identify robust pricing policies. The expected performance and corresponding variability of the facility is evaluated under each pricing scheme for different demand profiles. The focus of this paper is on non-correlated demand uncertainties (i.e. the number of arrivals during a given time interval is independent of the number of arrivals in the preceding and following time intervals), which we model by considering the number of arrivals in each minute as independent random variable with known distribution and time-of-day dependent mean. The performance model for a given demand realization is deterministic. The results show that a fixed toll can achieve about two thirds of the benefit of an ideal HOT system. The performance of a pre-scheduled toll system is between the fixed toll and the ideal system: closer to the ideal when the coefficient of variation is below 40%, and closer to the fixed toll otherwise. A relatively simple real-time system, with density-based linear adjustment to the pre-scheduled toll, has practically equivalent performance to the ideal system.