# An Assessment Scheme for Road Network Capacity under Demand Uncertainty
to traffic network performance evaluations and traffic design [4; 5; 6; 7]. The reserve capacity method considers the impact of traffic demand spatial distribution on the overall network capacity. It is more reasonable than the max-flow min-cut theorem. However, this method assumes that traffic demands in all directions grow at the same rate and the demand structure remains unchanged. Consequently, the fixed O-D matrix has a significant impact on the solution of capacity. With the development of the research on network capacity, an increasing number of scholars have realized that the spatial structure of traffic demand is variable and that changes in demand pattern have a significant impact on network capacity [8]. To reflect this influence, it is assumed that changes in traffic demand patterns, which may result from changes in both the total volume of traffic demand and the spatial structure, are allowed. Accordingly, the concepts of ultimate capacity and practical capacity were proposed, which provide improvements and extensions to the reserve capacity model [9]. The concept of variable demand type for road network capacity has been developed and applied [10; 11; 12; 13]. However, in practical application, changes in the external data may cause changes in initial demand or newly increased demand distribution parameter values, and the network capacity result will no longer be a fixed value when considering these changes. Therefore, it is essential to further analyze the uncertainty of demand parameters in the study of road network capacity and identify a suitable index for evaluating the traffic network's capacity under all possible uncertain parameters. It is generally believed that the uncertainty in the transportation network mainly derives from three aspects: travel demand, network supply, and travel choice behavior [14]. This study focuses on how demand uncertainty affects the entire transportation network capacity. Demand uncertainty is defined as travel demand fluctuations caused by time factors, special activities, population characteristics, traffic information, etc., which may lead to the periodic congestion of transportation systems [15]. The exact O-D demand da-ta are difficult to accurately obtain for traffic planning and management. It is typically important to assume that O-D demand is a known fixed value while researching traffic network issues. However, the deterministic demand obtained through surveys or forecasts may not be consistent with the real situation. Ignoring demand uncertainty can result in overestimations of network performance in transportation network models. Therefore, an increasing number of scholars are introducing demand uncertainty factors into research on traditional transportation problems. In the aspects of traffic network design and optimization, it includes the traffic equilibrium model [16], bus route optimization [17], multimodal transportation route optimization [18], and hub-and-spoke airline network design [19]. In addition, much logistics network research has considered the demand uncertainty, such as the location of urban-rural logistics integration design [20], urban subway underground logistics system layout problem [21], and multimodal logistics network design problem [22]. To consider the demand uncertainty in a traffic optimization model, we must introduce demand variables into the modeling process. Current uncertainty optimization theory consists of three main approaches: stochastic programming, robust optimization, and fuzzy programming [23]. To ensure that the system performance is within an acceptable range, these three methods consider all possible values of the uncertain parameters while seeking the optimal solution under the condition of constraints. In this study, an approximate method based on a sensitivity analysis is proposed as a solution to the inefficiency of the repetition capacity loading method. The sensitivity-analysis-based (SAB) approximation method is a heuristic solution strategy.