Lebedeva O. A. Dinamicheskoye modelirovaniye optimal'nogo marshruta v mul'timodal'noy transportnoy seti [Dynamic modeling of the optimal route in the multimodal transport network]. *Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie* [*Modern Technologies. System Analysis. Modeling*], 2020, Vol. 65, No. 1, pp. 44–50. 10.26731/1813-9108.2020.1(65).44-50

10.26731/1813-9108.2020.1(65).44-50

The task of optimizing the route transport system has been widely studied for the road network, but less tested for the urban public transport system. The multimodal route networks laid along the shortest path are able to reduce system performance at the time of reaching maximum throughput. The main objective of the study is to develop a dynamic model of the optimal route system for a multimodal transport network. A multimodal transport network is represented by a multilevel oriented graph with many nodes and arcs, which is modeled as a multilevel structure, where each level represents a unimodal subnet and is connected by lines. The network is modeled to simulate passenger movements and operations of transit vehicles. The task of a dynamic system optimization is formulated as the problem of variational inequality for the dynamic equilibrium of a user from the point of view of time-dependent marginal costs. The calculation of the unsteady marginal cost of the journey is based on the additional waiting time for passengers due to denied boarding on arriving vehicles. Therefore, the path is represented by an acyclic directional route on a multi-level oriented graph connecting a pair of departure-destination points. A transfer is considered because of vehicle capacity limitations. The dynamics of the transport system is studied by applying a multi-agent approach to account for operations and the process of waiting for passengers at stations (stopping points). The proposed algorithm is based on the solution of the general problem of the dynamic distribution of the transport flow. The method is a stochastic optimization algorithm for solving combinatorial problems. It links a stochastic mechanism to generate feasible solutions and iteratively improves quality based on performance. The algorithm relies on minimizing the distance (cross-entropy) to the unknown optimal equilibrium density. An experimental study of the solution of a dynamic problem is carried out on a small multimodal transport network. In most cases, the method for solving the dynamic optimal routing problem gives real results. As expected, with increasing load factor, the travel time of the route increases. This is due to the fact that, as the level of congestion increases, some users may be offered a longer route to reduce the total travel time. Since the possible routes for redistributing passengers are relatively limited, the percentage increase in overall time savings becomes not very significant when the system is heavily overloaded. Numerical research provides a basis for comparing optimal system routing at various congestion levels.

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