Models from Queueing Theory, in particular, polling models can be found in different application fields, such as telecommunications systems [1], industry, economy, etc. Priority queueing systems are a large class of queueing systems where the requests that enter into the system are distinguished by their importance. Priority Discretionary Discipline (DD) has its origin in the Jaiswal’s monograph (1973), where it is studied regarding problem of service with one server and two flows of requests. This discipline is more flexible than classical disciplines of preemptive (absolute) and head-of-the-line (relative) priority disciplines, which are characterized by a high level of conservatives. For two flows of requests, the DD discipline, following [2], it is described as follows: if the service time of a request is less than set value µ, then it achieved the absolute priority, otherwise - relative. Throughout time, new analytical and numerical methods have been developed, and important results have been achieved in this direction. We will mention only some scientific works devoted entirely or partially to mentioned models. These are the papers: M.I. Volkovinski and A.N. Kabalesky (1981), G.K. Mishkoy (1978), V.P. Dragalin and G.K. Mishkoy (1984), G.K. Mishkoy [3], where the discipline DD is analyzed more generally. Namely, it is supposed that the number of priority classes is arbitrary; it is assumed that service process of switching from one class of requests to another requires to spend some time for switching; the duration of switching is a random variable with an arbitrary distribution function; it allows to model and analyze different waiting times that objectively takes place in real systems. Numerical algorithms for busy periods and auxiliary characteristics [4] are elaborated and numerical results for concrete distribution of service and switching are obtained. The elaborated algorithms can be applied at the determination others performance characteristics (probabilities of states, queue length, etc.), in whose expressions the busy period is involved.