Application of the logistic regression for determining transition probability matrix of operating states in the transport systems

Abstract

Transport companies can be regarded as a technical, organizational, economic and legal transport system. Maintaining the quality and continuity of the implementation of transport requisitions requires a high level of readiness of vehicles and staff (especially drivers). Managing and controlling the tasks being implemented is supported by mathematical models enabling to assess and determine the strategy regarding the actions undertaken. The support for managing processes relies mainly on the analysis of sequences of the subsequent activities (states). In many cases, this sequence of activities is modelled using stochastic processes that satisfy Markov property. Their classic application is only possible if the conditional probability distributions of future states are determined solely by the current operational state. The identification of such a stochastic process relies mainly on determining the probability matrix of interstate transitions. Unfortunately, in many cases the analyzed series of activities do not satisfy Markov property. In addition, the occurrence of the next state is affected by the length of time the system remains in the specified operating state. The article presents the method of constructing the matrix of probabilities of transitions between operational states. The values of this matrix depend on the time the object remains in the given state. The aim of the article was to present an alternative method of estimating the parameters of this matrix in a situation where the studied series does not satisfy Markov property. The logistic regression was used for this purpose.