# Evaluating the Capacity Coordination in the Urban Multimodal Transport Network
## 1 Introduction  
The multimodal transport concept was first proposed by the United Nations in 1980 [1], defined as \"carriage of goods by at least two different modes of transport\". Transport systems, which take the form of multimodal transport networks, have become a hot research topic with rapid development [2]. In the past few decades, due to the swift growth in population across the world, the transport system has been expanded to meet the continuously increasing travel demands in urban areas [3]. Most urban commuters tend to be involved in various transport modes with the rapid development of information and telecommunication technology [4]. A typical urban multimodal transport network consists of different transport modes, especially roadways and railways. For the urban multimodal transport network, which is regarded as efficient, it is self-evident that the different sub-transport networks should be highly connected, synchronized, and complementary to each other in terms of network capacity and travel utility. Unfortunately, this is rarely true due to the complexity of coordination among different networks and the changing demand of individual demand over time. Today, many components of the urban multimodal transport network are highly congested. Commuting transport is one example; during the morning peak hour, the commuting transport on roads is congested, and the transit network is also very crowded, especially in China's large cities with a large population, such as Nanjing. A multimodal transport network is a complex network composed of different transport agents, including multiple nodes, edges, and transfer nodes. Each node contains a different capacity, and they together constitute the capacity system of the multimodal transportnetwork. Only when the flow exceeds the capacity threshold of the transport network can it cause congestion. Compared with the unimodal transport network, travelers always want to choose the mode or route with the smallest generalized cost. However, as the passengers who choose a single network increase, the generalized cost will increase, which will lead to travelers considering another network, thereby achieving the equilibrium of the entire multimodal transport network. Once a node fails, the risk will spread rapidly to the associated nodes, which will cause multiple node failures in the multimodal transport network, causing network paralysis, affecting the speed and quality of passenger transport, and affecting the normal operation of social economy. That is to say, when the nodes in the transport network are affected by internal or external factors, the load on the failed nodes will transfer to the associated adjacent nodes. Once the capacity coordination of nodes in other sub-networks is exceeded, it will lead to cascade failure such that the risk has an impact on the whole transport network, such as traffic congestion. Therefore, a study of the capacity coordination of the multimodal transport network can help understand the effectiveness of passenger flow transfer and traffic flow diversion in a multimodal transport network, which is conducive to the balance of passenger flow in multimodal transport, a reduction in network node inefficiency after overload, and effective management of a multimodal transport network. The performance of an urban multimodal transport network is limited by its capacity. [PERSON] et al. [5; 6] defined the theoretical capacity of a railway corridor as the maximum number of trains that can travel across a bottleneck section in a specified period. The capacity of a road, according to [PERSON] et al. [7; 8], is the maximum traffic volume that can be achieved over a given period. Road capacity is similarly defined in the Highway Capacity Manual (HCM) [9] as the maximum hourly rate at which persons or vehicles can traverse a point or uniform section of a lane or roadway in a given period. [PERSON] et al. [10] presented a conceptual framework to evaluate the capacity of multimodal freight transportation system.