Potentials Method for Mn/Gn/1/r and Mn/Gn/1/∞ Queueing Systems with Typical Dependences of the Input Flow Intensity on the Number of Customers

The application of the potential method to finding the stationary distribution of the number of customers in the M n / G n /1/ r and M n / G n /1/∞ queueing systems with threshold operation strateges is proposed. The dependences of the input flow intensity on the number of customers are considered, which are characteristic both for closed systems, which are models of the reliability theory, and for queueing systems with random rarefaction of the input flow. Service intensity control strategies are constructed on the assumption that the intensity can vary at the time when servicing starts. Formulas to determine Laplace transforms of the distribution of the number of customers in the system during the busy period and for calculating the average duration of the busy period are obtained.