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Mathematical modelling is a powerful tool that can be used to describe and understand complex real-world phenomena through the application of mathematical equations, algorithms, and simulations. Mathematical modelling of traffic flow plays a crucial role in understanding and predicting the dynamics of vehicular movement on roads. Usual modelling of traffic flow is restricted to treating traffic as an inorganic system. In this work, we bring in another layer of parameters that can affect traffic - human behaviour. Here we argue that a mathematical model with behavioural components could provide a more real-world understanding of traffic flow. The primary aim of the research is to create a mathematical model that incorporates human behaviour. [ABSTRACT FROM AUTHOR]

In industrial applications, many systems present serious productivity problems due to limited resources. Generally, the dynamics of resource allocation are inherently discrete-event driven, such as the buffer allocation in production line systems. In this paper, we develop a discrete-event mathematical model for resource allocation optimization. In this work, we consider two crucial optimization objectives, e.g., deadlock-free and efficiency, that originate from the customer's actual requirements. The main aim is to develop a resource allocation scheme for fulfilling the production process (without deadlock) while ensuring that the cost of the process is minimized. As a case study, we consider the vehicle scheduling problem in a signal-free intersection. The intersection is divided into several disjoint spatial traffic resources, and vehicles need to occupy different traffic resources for passing through the intersection. Thus, the traffic control problem at the signal-free intersection is transformed into a scheduling problem with limited resource constraints. An online control approach is developed to schedule vehicles to go through the intersection safely and efficiently by optimizing the resource allocation order. Simulation results demonstrate the efficiency and robustness of the proposed model and optimization approach. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mathematical modeling of traffic flow in a large automobile network. A statistical model of traffic flow proposed by the authors and designed for full-scale modeling of the operation of large-scale transport systems on long time intervals is used. A model has been constructed for one of the sides of the Moscow Ring Road and experiments have been carried out for two ways of jamming on the highway. The functionality of the naive entry control model has been tested in both types of the experiments. It has been shown that even the simplest method of limiting the incoming flow is efficient in terms of highway travel time losses. [ABSTRACT FROM AUTHOR]