Device and method for outputting navigation information, and vehicle

An apparatus that outputs navigation information for a vehicle, the apparatus comprising:

• at least one input interface, via which position data is provided including information with respect to a present position of the vehicle, destination data including information with respect to a destination position of a destination being traveled toward by the vehicle, and parking data including information with respect to at least two parking space positions and an availability of parking spaces at the at least two parking space positions;
• a data processor programmed to determine a sequence in which at least a part of the at least two parking space positions is to be approached based on the position data, the destination data, and the parking data such that the sequence meets an optimization criterion, and at a same time to check for at least one of the parking space positions whether the optimization criterion can be met by waiting at the at least one parking space position or returning to a parking space position to be approached chronologically before the at least one parking space position;
• and
• at least one output interface, via which the sequence can be output as navigation information;
• wherein the data processor is designed to determine whether the optimization criterion can be met by returning to a parking space position to be approached chronologically before the at least one parking space position in consideration of a conditional availability of parking spaces at the parking space position to be approached chronologically before the at least one parking space position, which results from a second availability model, which depicts the chronological development of the availability of parking spaces at the parking space positions to be approached chronologically before the at least one parking space position;
• and
• wherein the second availability model, which is based on a Markov chain, relates a parking rate, according to which parking spaces are occupied at a parking space position, to an availability rate, according to which parking spaces become available at the parking space position.

A method for navigation of a vehicle, the method comprising:

• providing position data including information with respect to a present position of the vehicle;
• providing destination data including information with respect to a destination position of a destination being traveled toward by the vehicle;
• providing parking data including information with respect to at least two parking space positions and an availability of parking spaces at the at least two parking space positions;
• determining a sequence, in which at least a part of the at least two parking space positions is to be approached based on the position data, the destination data, and the parking data such that the sequence meets an optimization criterion, and at a same time is checked for at least one of the parking space positions whether the optimization criterion is met by waiting at the at least one parking space position or returning to a parking space position to be approached chronologically before the at least one parking space position;
• and
• outputting the sequence as navigation information;
• wherein whether the optimization criterion can be met by waiting at the at least one parking space position is determined in consideration of costs which result from a first availability model, which depicts a chronological development of the availability of parking spaces at the at least one parking space position.