Passenger rolling stock scheduling to the passenger train timetable is based on the same type and number of carriages, which is the standard way of passenger trainset assignment. The possibility of train scheduling with a single carriage, a group of carriages or a railcar is topical issue for each carrier engaged in rail passenger transport in order to reduce the required rolling stock fleet. The paper presents an original network model developed for rolling stock scheduling for trainsets. The model makes possible to determine the optimum distribution of rolling stock in trainsets minimizing downtime at stations through the out-of-kilter algorithm. The model developed is applied to the scheduling of trainsets in part of the railway network in Bulgaria served by BDZ Passenger Transport Enterprise at the Plovdiv region. The use of the model allows to save passenger rolling stock and increases the efficiency of passenger rolling stock operation.