Sustainable Operational Efficiency Analysis of Long Steep Upgrades Considering Probabilistic Truck Bottlenecks

Conventional static indicators such as passenger car equivalent (PCE) factors cannot adequately capture the dynamic bottleneck effects caused by truck speed degradation on long steep freeway upgrades. To address this issue, this study proposes an operational efficiency analysis framework integrating truck crest-speed reliability and microscopic simulation. Vehicle trajectory data were collected using unmanned aerial vehicles, and truck power-to-mass ratio data were obtained from the Chinese truck market to establish a representative truck model. Monte Carlo simulation was employed to quantify crest-speed reliability, whose complement (failure probability) characterizes the likelihood of truck bottlenecks arising. A calibrated VISSIM simulation model was then developed to reproduce truck climbing speed degradation and microscopic driving behavior on long upgrades. Finally, a response surface model was constructed using average delay as the operational efficiency indicator. The results indicate the following: (1) As grade length increases, the probability of truck bottleneck occurrence gradually rises, and the marginal effect of this increase becomes more pronounced with steeper grades. Specifically, truck crest-speed reliability exhibits a nonlinear decreasing trend with increasing grade length. For example, under a design speed of 120 km/h and a 95% reliability threshold, the corresponding grade length for a 2.5% grade is 1367 m, whereas for a 4% grade it drops to 232 m, representing a reduction of 83%. (2) Under high traffic volume conditions, an increase in truck proportion leads to a significant rise in average delay (up to 17.54 s). Although improving crest-speed reliability reduces the probability of truck bottleneck occurrence and partially mitigates delay, it cannot fully offset the traffic pressure induced by high traffic demand. Grade and grade length remain the most critical factors driving operational efficiency deterioration, with a maximum impact on average delay of 38.72 s. (3) The response surface model reveals significant interaction effects between traffic volume and truck proportion, as well as between traffic volume and crest-speed reliability, indicating that traffic demand plays a dominant role in amplifying the impact of truck bottlenecks. The framework proposed in this paper provides probabilistic quantitative decision support for sustainable longitudinal grade design and freight traffic management on mountainous freeways.