Tendencies of the $M_r|G_r|1|\infty$ model’s study

The article is a short review of a queuing model $M_r|G_r|1|\infty$. First of all, methods for analysis of the $M_r|G_r|1|\infty$ model’s characteristics with classic disciplines such as pre-emptive, head-of-the-line and alternating priorities are presented. A transition to analysis of parametric disciplines and further to class of conservative disciplines is justified and implemented. Special attention is paid to conditions for existence of stationary distributions and preservation laws. Particularly, two new preservation laws for stationary distributions of queue lengths are established. The range of optimization problems for the class of conservative disciplines and some of its subclasses are presented. Directions of asymptotic analysis under different traffic intensities are described. A new result for stationary waiting time distributions in terms of Laplace–Stilties transform is formulated in case of Kleinrock’s parametric discipline.