## 5 Numerical Analysis
### Cost Comparison  
This section analyzes the potential impact of static wayfinding instructions on network flow under various conditions. We explore the patterns of cost changes for different types of links and provide a detailed analysis of the relationship between user perception and actual cost changes. Finally, strategies to aid decision-making in traffic management are discussed, particularly focusing on optimizing the placement of wayfinding instructions to enhance network efficiency and user experience. Four static wayfinding instruction placement schemes are analyzed in the same real-world network: scheme 1: no static wayfinding instructions; scheme 2: placement scheme as depicted in above Figure 7; scheme 3: placement scheme as depicted in Figure 10; and scheme 4: placement scheme as depicted in Figure 11. Scheme 2 serves as a reference condition, scheme 3 illustrates the scenario where static wayfinding instructions are placed near  
Figure 9: Convergence performance of applied step size determining method. the destination, and scheme 4 illustrates the scenario where static wayfinding instructions are placed farther from the destination. Figure 11: Sioux Falls network with implementation of static wayfinding instructions (Scheme 4). Figure 10: Sioux Falls network with implementation of static wayfinding instructions (Scheme 3). In scheme 2 and scheme 4, the costs of directly guided links increase while the costs of directly guided links remain unchanged in scheme 3. Static wayfinding instruction as a type of traffic control device can help reduce users' uncertainty. However, under certain conditions, user perception may not change due to static wayfinding instructions because users are assumed to have a certain level of information on link travel time cost in the GNL model, even if the information is inaccurate. Consequently, static wayfinding instructions guiding links with obvious lesser cost will not influence the flow and cost significantly when preventing unfamiliar users from incorrect links (i.e., most users' link choices will not differ regardless of whether guiding information is provided at this node). In Scheme 3, since the guiding direction to the destination aligns with most users' existing knowledge, the overall network cost remains unchanged after placing the two static wayfinding instructions. Additionally, compared with scheme 1, the static wayfinding instructions in scheme 4 are positioned significantly farther from the destination. Consequently, the travel time costs on links have greater changes in scheme 4 than in scheme 1. The user's wayfinding process is a multistage decision problem that follows the Bellman optimality principle and can be decomposed into smaller subproblems. For example, in the Sioux Falls network, a path from node 1 to node 23 that passes through node 15 can be decomposed into two segments: the path from node 1 to node 15 and the path from node 15 to node 23 when analyzing the user's wayfinding process. In scheme 1, static wayfinding instructions placed in front of nodes 15, 20, and 24 will not affect the wayfinding process for paths originating from nodes far from 15, 20, or 24, which results in a localized impact on traffic flow. In contrast, in Scheme 4, the static wayfinding instruction placed in front of node 3 significantly influences the choice probabilities of many paths over a larger area, leading to a substantial increase in the total travel time cost across the network. Based on the above discussion, some static wayfinding instruction placement strategies can be further considered. First, placing instructions in alignment with users' perceptions can reduce disruptions to network flow while guiding unfamiliar users away from incorrect paths. When multiple links belong to paths with similar costs, careful consideration is needed in the placement of static wayfinding instructions.