The present article considers one of a number of models of a randomly loaded system with limited buffer storage. Tasks with random volume arrive in the system at random moments of time. If there are no places in buffer storage following the arrival of a succeeding load, the system is assumed to be blocked. There are short-term halts related to faults in the system. Through application of the apparatus of semi-Markov walk processes, the Laplace transformation of the distribution of the first moment of the blocking time of the system is found for this model, and expressions for its mathematical expectation and variance are obtained in explicit form.