Model of an Unsignalized Intersection in the Form of Queueing System with Batch Arrival Process and Unreliable Server

In the paper, a mathematical model of a non-equal priority intersection of single-lane roads represented as a single-server queuing system with a batch Poisson arrival process and unreliable server. The study focuses on the passage of vehicles from the secondary road and the resulting queue. The traffic flow on the main road is modeled as the state of the server like "on/off" mode, determined by a given Markov chain. A system of Kolmogorov differential equations was constructed, and the generating function method was applied to solve the system. Additionally, the condition for the existence of a stationary regime of the system was found. As a result, the steady-state probability distribution of the number of customers is derived. Numerical experiments are conducted.