Development of a method for modelling delay propagation in railway networks using epidemiological SIR models

Abstract

A method has been developed to simulate propagation of train delays in branched railroad ranges using modified epidemiological SIR models. These models take into account the mutual influence of trains with different priorities in the flow. This makes it possible to study the heterogeneous dynamics in the propagation of delays among trains of different priorities. To consider the propagation of the primary delay in space and time, it is proposed to represent the topology of the railway network in the form of an undirected graph with reference to the edge of the graph in the mathematical system of differential equations of the SIR model. This unifies the process of constructing SIR models for each edge (section) of the network graph and reduces the dimension of the problem. To take into account the influence of the "network effect", it is proposed to determine the transit coefficient for each station of the section. This coefficient helps calculate the number of delayed trains for adjacent sections. To set SIR models, it is proposed to use empirical data on the propagation of the average delay in the standard traffic schedule in the corresponding section. For the sequential solution of SIR models corresponding to interconnected network sections, an algorithm is applied to turn the network graph into a directed tree the root of which is the station where the delay occurs. Tests on modelling the propagation of train delays in the railway network are carried out taking into account the mutual influence of different categories of trains in the flow and the built-in time reserves for the restoration of movement. The obtained simulation results have confirmed the adequacy of the solutions and helped quantify the influence of primary delays and the amount of time reserve in the schedules of trains of various categories on the reliability of the standard train schedule

Modelling railway delay propagation as diffusion-like spreading

“…Still, there are examples to be found. One example is Gurin et al (2020), which show that classic Susceptible-Infected-Recovered (SIR) modelling applied to railways help understanding primary delay evolution, making use of 'transit coefficients' to account for spreading of delays to adjacent stations [12]. Another example is the paper by Monechi et al (2018), which approaches the problem from a data perspective and infers 'laws' of railway delay propagation [11].…”

“…An approach which is conceptually similar would be to shift perspective and define total delay on edges instead of stations, e.g. analogous to [12]. Such a model would automatically include the inherent directionality of trains.…”

“…Alternatives to such purely data-driven methods can be found in models where mechanisms of delay propagation are explicitly implemented. For example, Monechi et al analysed the German and Italian railways and found a set of 'laws' that drive the spreading of delays [11] and Gurin et al simulate train delay propagation using modified SIR models [12], both containing analogies to epidemic spreading models. Also beyond railways, models with contagion processes are used to simulate transportation and congestion [13].…”

Research on traffic congestion situation in urban central area based on SIR model

“…Shi, Z. et al [7] used SIR model to simulate the propagation process of rail transit passenger congestion, found that the propagation rate affected the passenger congestion rate, and put forward policies to control passenger congestion from the two aspects of supply control and demand control. Gurin, D. et al [8] used the improved SIR model to simulate the train delay propagation process in the railway network, and studied and considered the delay propagation between trains with different priority levels. Zhao, Y. et al [9] established the SIR model of multi station fault delay propagation in urban rail transit operation, predicted the spatial impact range of station delay, and provided the basis for the safe operation of rail transit.…”