Semi-Markov model of multi-modal transport operation

Multi-modal transport means the transport of the objects through at least two different carriers of any combination of simple tasks of transport carriers (by truck, by train, by ship or by plane). A Semi-Markov (SM) model of multi-modal transport operation is presented in the article. The SM process is defined by the renewal kernel of that one. In our model, time to failure of the operation is represented by a random variable that denotes the first passage time from the given state to the subset of states. The duration of one operation cycle is a random variable representing the return time to the initial state. The appropriate theorems of the Semi-Markov processes theory allow us to calculate characteristics and parameters of the transport operation model. The article presents the example of the transport operation final part of container with cargo from Warsaw to Stockholm, where from Warsaw to Gdynia, the container is transported by lorry, from Gdynia to Karlscorona by ferry and from Karlscorona to Stockholm by truck.