The way trains are organised and run affects the quality of the journeyJourney. The mathematical modelMathematical model of the nineteen sub-criteriaSub-criteria assesses the following aspects: departure and arrival of train at the scheduled time, delivery of meals to passengers, provision, layout, and condition of bed linen, ordering of food and drinks from the dining-carDining-car and delivery to the compartment by carriageCarriage attendantAttendant, on-board delivery of popular newspapers and magazines, on-board internetInternet access, on-board ticket purchase option, dining-carDining-car reservations, taxiTaxi call facility, on-board card payment option. The model also assesses aspects such as souvenirSouvenir shopping on the train, meeting passenger preferences for on-board music and in-train information, securing passenger luggage and belongings on board the train, purchasing overseas medical insuranceMedical insurance on board the train, obtaining a visaVisa at the frontier point, the appearance of the train staff, communication culture of train service staff with passengers and other members of staff, proficiency in foreign languagesForeign language of the train staff, competence, objectivity and communication skills of customs officers and frontier guards. A numerical example with real train data shows the adequacy of the mathematical modelMathematical model. It can be used by quality assessors in rail passenger transport companies as well as by train tour operators and technology developers.