Service systems as traffic models and applications to environmental problems

Pospelov Pavel Ivanovich, Tatashev Aleksandr Gennadyevich, Terentyev Alexey Vyacheslavovich, Trofimenko Yury Vasilyevich, Yashina Marina Viktorovna

This paper examines the application of the theory of queuing in the modeling of traffic flows. When modeling traffic flow using a service system, it is usually assumed that the application corresponds to a vehicle. Such queuing models are most often used when analyzing traffic at the intersection of roads. In addition to models of this type, this paper considers service models that have a different interpretation. For example, when representing a traffic flow in the form of particles moving along a discrete grid, the flow characteristics are studied using a queuing network in which the particles correspond to the serviced nodes, and the free grid cells located in front of the particle represent applications that are in the queue of this node and waiting for service.

Keywords:mathematical traffic models, traffic flows, queuing systems and networks, transport ecology, road safety, traffic organization at intersections, random processes with prohibitions.