Which extension is used to solve transportation network analysis problems in ArcGIS?

The Network Analyst extension is specifically designed to address transportation network analysis problems within ArcGIS. This extension allows users to perform complex analyses related to network data, including routing, service area analysis, closest facility searches, and origin-destination cost matrix computations. By leveraging the capabilities of the Network Analyst, users can analyze various aspects of transportation systems, making it an invaluable tool for tasks such as optimizing route selection and determining the best locations for services based on travel distance or time.

In contrast, the other extensions mentioned do not focus on transportation network problems. The Image Analyst extension is primarily used for advanced image processing and analysis, while the Geoprocessing extension provides general tools for data manipulation and analysis without a specific focus on transportation networks. The Geodata extension is aimed at managing and sharing geographic data but does not inherently involve transportation analysis features. Thus, the Network Analyst extension stands out as the quintessential tool for solving transportation network analysis challenges in ArcGIS.