A method for influencing a traffic management system with a traffic control computer which controls a plurality of alternating light signal systems in a traffic network for the purpose of a priority control for at least one emergency vehicle with right of way, wherein the influencing of the traffic management system takes place on the basis of current position data and a direction of travel vector (R') of the at least one emergency vehicle in order to accelerate its travel on a projected travel route, the process comprising the steps of: a) providing position data of a destination for the at least one emergency vehicle; b) providing the current position data and the data of the current direction of travel vector (R') of the at least one emergency vehicle; c) predicting a route of travel for the at least one emergency vehicle from its current position to the position of the destination, taking into account the direction of travel selected by the driver of the emergency vehicle and represented by the direction of travel vector (R'); d) influencing the alternating light signal systems concerning a projected direction of travel on the projected travel route in such a way that the respective alternating light signal system gives way for the traffic in the direction of the projected travel route before or on the predicted arrival of the at least one emergency vehicle, chacterized, in that in a step d') carried out in or before step d) further alternating light signals systems which do not directly relate to the projected direction of travel of the emergency vehicle and which are located in the surroundings of the alternating light signal systems in front of the emergency vehicle concerning the projected direction of travel on the projected travel route, are switched in such a manner that vehicles located in a driving corridor of the at least one emergency vehicle on the lane of the projected travel route can leave the driving corridor and that no vehicles can enter the driving corridor until the at least one emergency vehicle arrives at this location, so that the at least one emergency vehicle pushes a sphere of influence of the priority control along the projected travel route, in which sphere of influence a drain of traffic away from the driving corridor is effected along the projected travel route in addition to a green wave. a) providing position data of a destination for the at least one emergency vehicle; b) providing the current position data and the data of the current direction of travel vector (R') of the at least one emergency vehicle; c) predicting a route of travel for the at least one emergency vehicle from its current position to the position of the destination, taking into account the direction of travel selected by the driver of the emergency vehicle and represented by the direction of travel vector (R'); d) influencing the alternating light signal systems concerning a projected direction of travel on the projected travel route in such a way that the respective alternating light signal system gives way for the traffic in the direction of the projected travel route before or on the predicted arrival of the at least one emergency vehicle,