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Marine passenger ports are integrated into the transport systems of cities and regions today. If there are sufficient developed mathematical forecasting models in the class of polynomial models, probability series, and a number of others, then the models describing the influence of the external environment on ferry market are not sufficient. The developed scheme of interaction between the participants of the cruise market and the mathematical model of the port as a technical system is presented in this research. The article substantiates new purposes to use the logistic function to assess the external environment. A mathematical model and the derivation of the new basic equation of the logistic function for ferry market are given. Analytical data were collected on the ports and terminals of the Adriatic Sea and the Baltic Sea, and data were selected of ship calls at the passenger port St. Petersburg "Marine Facade" (2019-2020). The article proposes the consideration of new various proportionality factors that will determine the demand for cruise transportation modeling in the short-term forecasting interval. A complete mathematical model is given taking into account the real schedule of the sea passenger port. The logistic function proposed in the article allows us to solve the forecasting problem in a new way in relation to the selection and evaluation of a cruise product. Moreover, it allows us to solve a group of economic problems related to promotion problem for particular cruise product on the market, allows us to evaluate the activity of passengers when they are choosing a cruise product, and allows us to make adjustments to the planned port working schedules and to make timely adjustments. The main advantage of the proposed model is an analytical assessment of the effect of the external environment, both on passenger ports and on ferry and cruise companies. [ABSTRACT FROM AUTHOR]