In past studies on the combined modal split and traffic assignment (CMSTA) problem, there are problems of not considering the three critical factors simultaneously: the user equilibrium (UE) on the transit network, the interaction of modes, and the captive demand. In this paper, a CMSTA model that considers the three critical factors simultaneously is presented. In the model, both the equilibrium on the auto network and the equilibrium on the transit network are considered, the interaction of the auto flow and the transit flow on link travel time is considered, and the captive demand of each mode is considered. An algorithm incorporating the double-stage algorithm, the diagonalization algorithm, and the gradient projection (GP) algorithm is presented for solving the model. The model and algorithm were applied to two networks and their validity is shown. The resultant OD demand for both modes is different with different captivity parameters. When the captivity parameter for auto is fixed, the resultant OD demand for the buses increases with the increase of the captivity parameter for the buses whereas the resultant OD demand for the autos decreases with the increase of the captivity parameter for the buses. The model applies to a city with two transportation modes: auto and bus. They are useful in the travel demand analysis and transportation planning and management.

Knowing the temporal and spatial equilibrium (TSE) flow is the basis for transportation planning and management of each mode (ocean, air, rail, road, logistics, etc.). It also helps to alleviate congestion of each mode on a transportation network. The current methods in transportation planning only consider the spatial equilibrium of flow on the network. A method for obtaining the TSE of flow on a transportation network is rare. In this paper, a one-level variational inequality (VI) model was presented for the TSE of flow on networks. A relaxation with multilevel gradient projection (GP) algorithm is proposed to solve the model, with the 1st level gradient projection for temporal equilibrium and the 2nd level gradient projection for spatial equilibrium. Given a temporal distribution of total flow for each origin-destination (OD), the spatial equilibrium can be reached with the 2nd level algorithm. The temporal equilibrium can be reached by splitting the total flow for each OD on the temporal dimension with the 1st-level algorithm. The application of the model and algorithm to two networks shows that the minimum path travel time of an OD is equal and minimal. It also shows that the total cost of all flows reaches a minimum and that flows reach equilibrium on temporal and spatial dimensions. Our paper is the first study able to show this and has great potential in transportation planning and management, or in balancing vehicles/vessels/planes, or goods on temporal and spatial dimensions to alleviate congestion. The algorithm does not need time-space network expansion and applies to real-size multiple-origin multiple-destination networks.

In the past studies, a road accident message was often broadcast by forming a Vehicular Ad Hoc Network (VANET), in which the safety message broadcasting methods often lead to broadcast storms. This study presented a method to broadcast accident messages in a travel guidance system (TGS) that avoids broadcast storms that avoids the need for vehicles to form an ad hoc network. Unlike most current methods, which disseminate messages to as many vehicles as possible, this method sends messages only to the exact vehicles that will be influenced by an accident. In the TGS, the transport center of a city sends messages of the optimal routes and alternative routes to travelers when they start their journey. In normal situations, vehicles run on the optimal routes determined by the transport center. When an accident happens in a street, the accidental vehicle sends a message to the transport center through 5G communication. The transport center looks up the vehicles with their original routes passing the accident location during the lasting time of the accident and sends a safety message to them. The influenced vehicles then select the alternative routes which are stored in their On-Board Unit (OBU) to avoid the accident. Vehicles not influenced by the accident receive no message. Thus the redundant and unnecessary dissemination of messages will be removed. The method presented in this paper is the only one that can thoroughly remove the unnecessary and redundant rebroadcast.

In some situations, drivers prefer to select the most reliable paths (MRP). In the minimum-delay routing problem in communication networks, signals need to be transmitted on the MRPs. Since a minimum cost path may not be an MRP, the traditional minimum cost path based user equilibrium does not apply to such scenarios. Therefore, the study of the connectivity reliability based user equilibrium (RUE) model which is based on the MRPs is needed. Unfortunately, none of the previous studies ever covered the RUE based on the MRPs. In this paper, a RUE variational inequality (VI) model based on the MRPs is presented. The path reliability is the multiplication of the reliability of the links on the path. A heuristic algorithm is presented to solve the VI model. A multiplication-based algorithm is used to find the MRP in the solution process. The model and algorithm are applied to two networks and their validity is shown. The method presented in this paper is useful for the emergency evacuation on transportation networks or the minimum-delay routing problem in communication networks.