Method of modelling operation and maintenance processes in public transport systems using a certain class of stochastic processes

The study presents a method for application of the theory Markov homogenous processes for modeling of the process of vehicle operational state changes characterized by exponential distribution of their duration time. A model of operation and maintenance of vehicles used in the research object has been developed. The research object is a city bus transport system situated in the analyzed agglomeration. Stochastic process {X(t), t = 0} is a mathematical model of the process of operation and maintenance of public transport buses. The analyzed stochastic process {X(t),t = 0} has a finite phase space S, S={S1, S2, ..., Sn}. It was assumed that operation of the model is to be described by the homogeneous Markov process {X(t) : t ? R+} with a finite set of S states. The states of the analyzed stochastic process correspond to the operational states distinguished for a bus. A hypothetical computing model was built in order to illustrate the discussion and present a method for application of the developed model. The parameters of the model were estimated based on the analysis of initial results of experimental tests conducted in a real bus transport system