The framework of licensed shared access (LSA) to spectrum seems to become one of the trends of 5G wireless networks. The framework assumes the simultaneous access to spectrum by at least two parties - the primarily owner (incumbent), which has the highest priority, and several secondary users (licensees), which have lower priorities. The critical up-to-date problem is the development of the corresponding radio admission control and load balancing algorithms that form an essential part of the LSA agreement between the parties. The algorithm of binary use of spectrum gives an absolute priority to the incumbent, e.g. the airport using spectrum for aeronautical telemetry purposes. In the paper, capturing the inhomogeneous in time nature of rates of requests for access to spectrum and average times of spectrum use, we propose a queuing model of binary access to spectrum as seen from the licensee's point of view. The queue is described by an inhomogeneous birth and death process with catastrophes and repairs. The main aim of the paper is to find the bounds on the rates of convergence to the limiting characteristics of the queue - average number of users, blocking probability, and probability of service interruption due to the incumbent's need for spectrum. Not only the acceptable upper thresholds on the limiting characteristics are important for consideration but also the corresponding bounds showing the moment in time when the system becomes stable and the LSA licensee could really access to spectrum.