Robust tolling schemes for high-occupancy toll facilities under variable demand

High-occupancy toll (HOT) lanes have become an increasingly prevalent form of congestion management pricing in the United States in the past few decades. The success of a HOT facility depends on the pricing scheme, which determines the utilization of the HOT lane, and the corresponding congestion relief on the parallel general purpose lanes. An additional complexity in determining HOT rates arises from the inevitable variability in travel demand inherent to transport networks. A successful tolling scheme must therefore be robust to changes in travel demand. Various tolling schemes for HOT facilities are examined in efforts to identify robust pricing policies. The expected performance and the corresponding variability of the facility are evaluated under each pricing scheme for different demand profiles. The focus is on noncorrelated demand uncertainties (i.e., number of arrivals during given time interval is independent of number of arrivals in preceding and following time intervals), which are modeled by considering the number of arrivals in each minute as an independent random variable with known distribution and time-of-day dependent mean. The performance model for a given demand realization is deterministic. Results show that a fixed toll can achieve about two-thirds of the benefit of an ideal HOT system. The performance of a prescheduled 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. The performance of a relatively simple real-time system, with density-based linear adjustment to the prescheduled toll, is practically equivalent to that of the Ideal system.