Modeling of production processes of vehicle care system using generalized geometric pattern representing possible states of the vehicle

Abstract

A new generalized model of vehicle maintenance and repair process for a vehicle care enterprise is suggested. The model regards a wide range of factors of modern enterprise as an automobile transport unit. The task is solved by applying mathematical models of the theory of reliability and queuing. Vehicle care enterprise is viewed as an open queuing system referring to a real-time enterprise. A geometric pattern representing possible states of the vehicle and its possible transitions is suggested to analyze the maintenance of the vehicle as a random process with discrete states. The transition state is discrete, but at random times. The performance of a vehicle in time is viewed as a continuous-time and discrete state system. Since most of the transition rate depends on the total distance travelled, the solution to the Kolmogorov equations is offered by considering numerical integration and Runge-Kutta methods. Resulting from the theory of Markov random processes the method of dynamics of average is applied to characterize the functioning of a group of vehicles. Being aware of possible performance of a vehicle, you can simulate functioning of a group of any number of vehicles. The release rate and annual mileage of a  j -age group vehicle are necessary to determine the functioning program of a car care enterprise.