The formalization of the process of coordinating the operation of different modes of urban passenger transport based on a network-dynamic model

Abstract

The quality of transport services for the urban population largely depends on the coordination of the operation of different modes of urban passenger transport (UPT) at transfer nodes and on common sections of the route network. As a result of excessive route duplication, uneven transport supply, and operational constraints in urban electric transport, disruptions in service regularity, rolling stock accumulation, and additional passenger time losses occur. Goal. The aim of this paper is to develop a formalized approach to the adaptive coordination of UPT operations across different modes based on a network-dynamic model. Methodology. The study combines a literature review of coordination in UPT, transfer node operation, service headway regularity, and synchronization models with the adaptation of the Kuramoto model of coupled oscillators to coordinate inter-route interactions in the UPT system. Each route is represented as a phase oscillator. The coupling matrix is constrained by the structure of the route network graph; that is, route interactions are considered only on common sections and at transfer nodes. Results. A network-dynamic model for coordinating the operation of different UPT modes is proposed. The Kuramoto order parameter is shown to be an indicator of the coordination component of transport service quality. The role of urban electric transport as a backbone oscillator with a fixed phase, relative to which the coordination of intermodal interaction of UPT is proposed to be carried out, is formalized. Three phase states of the system are distinguished: phase drift, chimera state, and phase locking. Originality. Unlike the classical Kuramoto model, the proposed approach accounts for the topological constraints of the route network via spatial-technological coupling and the specific features of intermodal coordination in UPT. It is substantiated that the target state of the system is not complete synchronization, but phase locking with regular service headways. Practical value. The model can be used to form an integrated system of adaptive dispatching control, allowing control actions to be differentiated by the system's current phase state, coordinating the arrival of rolling stock at transfer nodes, and reducing passenger time losses.