All the provisions of the California Toll Bridge Authority Act (Chapter 1 (commencing at Section 30000) of this division) applicable to toll highway crossings shall apply to the activities of the department and the authority in connection with the rapid transit tube insofar as they are not inconsistent with the provisions of this article. The provisions of said act shall not apply to the district and shall not require or permit the fixing of a toll by the department or the authority for the use of the rapid transit tube. The district shall have the sole and exclusive right to the use of the rapid transit tube in the absence of an agreement between the district and any other party for any use by such other party on payment of appropriate compensation to the district.