Among the micro-logistic transport systems, railway stations should be highlighted, such as one of the most important transport infrastructure elements. The efficiency of the transport industry as a whole depends on the quality of their operation. Such systems have a complex multi-level structure, and the incoming traffic flow often has a stochastic character. It is known that the most effective approach to study the operation of such systems is mathematical modeling. Earlier, we proposed an approach to transport hub modeling using multiphase queuing systems with a batch Markovian arrival process (BMAP) as an incoming flow. In this paper, we develop the method by applying more complex models based on queuing networks that allow us to describe in detail the route of requests within an object with a non-linear hierarchical structure. This allows us to increase the adequacy of modeling and explore a new class of objects—freight railway stations and marshalling yards. Here we present mathematical models of two railway stations, one of which is a freight railway station located in Russia, and the other is a marshalling yard in the USA. The models have the form of queuing networks with BMAP flow. They are implemented as simulation software, and a numerical experiment is carried out. Based on the numerical results, some “bottlenecks” in the structure of the studied stations are determined. Moreover, the risk of switching to an irregular mode of operation is assessed. The proposed method is suitable for describing a wide range of cargo and passenger transport systems, including river ports, seaports, airports, and multimodal transport hubs. It allows a primary analysis of the hub operation and does not need large statistical information for parametric identification.

The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.

A new approach to some optimization problems arising in the transport logistics was proposed. Consideration was given to the fundamental problems of the today logistics such as the problem of optimal arrangement and that of identification and segmentation of the logistic zones. They are solved using the “wave” method which relies on the analogy between the determination of the global extremum of the integral functional and propagation of light in an optically inhomogeneous medium. A numerical algorithm was developed, and the results of calculations presented.