Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8693On Analysis of M[X]|G|1|r Queuing SystemSamouylovK EКафедра систем телекоммуникаций; Российский университет дружбы народов; Peoples Friendship University of Russiaksam@sci.pfu.edu.ruSopinE SКафедра систем телекоммуникаций; Российский университет дружбы народов; Peoples Friendship University of Russia-Peoples Friendship University of Russia150120111919708092016Copyright © 2011,2011The paper presents results of analysis of M[X]|G|1|r queuing system with vacations and batch arrival. The relationship between the probability distributions of systems with infinite and limited capacity is shown. An expression for generating function of queue length distribution for the case of r < ∞ is obtained, as well as formulas for stationary probabilities, call loss probability and other characteristics.queuing systembatch arrivalvacationslimited queue lengthсистема массового обслуживаниягрупповое поступлениепрогулки прибораконечная очередь