In this paper we consider a model of information processing with two types of flows of customers—priority and non-priority. The service time of customers is random with an exponential probability distribution. The distribution parameters correspond to the customer type. Each type of customer has its own buffer, limited in waiting places. Information in the buffer is restricted by a time-to-live parameter, after which transmission of a customer may become irrelevant. Time-to-live parameter is a random variable that also has an exponential distribution. The contribution of the paper is to develop an algorithm for automatically calculating the stationary probability distribution. It allows to construct of coefficient matrices, simplify the one of the most intensive parts of working with priority systems manually. This algorithm provides the possibility of studying systems with priorities on large buffer volumes, which is extremely difficult to implement without automation.