Semi-Markov Model of the System of Repairs and Preventive Replacements by Age of City Buses

Abstract

The paper presents a mathematical model of the system of repairs and preventive replacements by age of city buses. The mathematical model was developed using the theory of semi-Markov processes. In the model developed, four types of city bus renewal processes are considered and three types of corrective repairs and preventive replacement. Corrective repairs are considered in two types: minimal repairs (repairs carried out by the Technical Service units) and perfect repairs (repairs carried out at the stations of the Service Station). The models of restoration systems that use semi-Markov processes in which minimal repairs, perfect repairs, and preventive replacements by age, have been examined in the literature to a limited extent. The system under consideration is analysed from the point of view of two criteria: profit per time unit and availability of city buses to carry out the assigned transport tasks. Conditions of criterion functions’ extremum (maximum) existence were formulated for the adopted assumptions. The considerations presented in the paper are illustrated by exemplary results of calculations.

Keywords

• city buses
• semi-Markov processes
• preventive maintenance
• corrective maintenance
• age-replacement
• minimal repair