## 1 Introduction  
In the past decades, rail transport has played an important role in responding to major emergencies such as armed conflicts, terrorist attacks, and natural disasters [1]. Numerous practices [2, 3, 4] have shown that using railways for cross-regional and long-distance land transport can improve emergency efficiency and shorten response time. However, due to the constraints of the rail infrastructure, railways cannot directly provide \"door-to-door\" services. Generally, the transport between the rail transshipment hubs (after this referred to as hubs) and origins or destinations requires assistance from road systems [5]. In other words, if railways are used for emergency transport, the combined transport of roads and rails will usually become an inevitable choice. Given this, it is of great practical value to study road-rail multimodal transport optimization from the emergency perspective [6]. Numerous studies suggest minimizing response time is the top priority in emergency transport decisions [7]. Generally, when considering the schedule of road-rail multimodal transport tasks, congestion at hubs (after this referred to as congestion) is an important issue that cannot be ignored. Unlike road transport, road-rail multimodal transport requires transshipment operations at hubs (i.e., transshipping cargo from trucks to trains, or vice versa). Due to the limited transshipment efficiency, queuing is usually unavoidable when the loading or unloading efficiency does not match the arrival rate [8]. In large-scale emergency transport, it is common for temporary freight demand beyond the capacity of the transport network [9]. If congestion cannot be effectively controlled when developing road-rail multimodal transport schemes, the waiting time for cargo to be transshipped at hubs (after this referred to as the waiting time) would be prolonged and negatively affect the overall schedule for emergency transport. In recent years, congestion management has become one of the hotspots in multimodal transport research. Existing literature [5; 10] mainly explores solutions from strategic and operational perspectives. From a strategic perspective, the supply of hub resources determines the transshipment efficiency of multimodal transport systems. Some studies [11; 12; 13] control congestion by adjusting the number and location of hubs or equipping hubs with appropriate transshipment facilities. Optimizing multimodal transport schedules becomes another natural choice when demand and hub capacity are known. At present, adjusting the arrival rate is the primary means at the operational level. For example, some studies [14; 15] provide the traffic flow limits of hubs, while others [16; 17; 18; 19] formulate the transshipment time or cost as a function of cargo arrival rate and hub transshipment efficiency. Studies on emergency-related multimodal transport [20; 21; 22] also follow these ideas. For example, Ref. [20] considered the damage on routes and hubs to propose an integrated approach for solving the post-disaster multimodal transport network recovery and relief supplies transport problem. To manage congestion, both perspectives were considered: Optimize the repair plan for damaged hubs first to further determine the transshipment efficiency of the hubs during the repair period and then adjust the arrival rate under the given transshipment efficiency. However, due to the lack of specific descriptions of transshipment operations, the above studies do not focus on the impact of the transshipment scheduling details on the waiting time. In fact, efficient transshipment scheduling can save the time that cargoes spend at hubs. Many multimodal transport studies have focused on this goal. For example, certain studies [23; 24] have optimized crane scheduling within hubs to minimize vehicle waiting time; other studies [25; 26] have improved yard storage strategies to reduce non-operational time, thereby enhancing transshipment efficiency; [PERSON], [PERSON] et al.