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)8231Research ArticleOn the Modeling of Queueing Systems with Multiple ResourcesNaumovV Avaleriy.naumov@pfu.fiSamuylovK EDepartment of Applied Informatics and Probability Theoryksam@sci.pfu.edu.ruPalveluinnovaatioiden kehityskeskus (Service Innovation Research Institute)Peoples’ Friendship University of Russia150320143606408092016Copyright © 2014,2014We consider queueing systems, in which customers occupy some resources that are released after customer departure. Arriving customers are lost if there is not enough free resources required for their servicing. In such systems for each customer it is necessary to record vector of occupied resources until its departure. This greatly complicates the stochastic processes describing the behavior of systems in time. Instead of systems of this type we propose to investigate their simplified analogy. Simplified system operates similarly to the original, except that the amount of resources released upon completion of service, is random and may differ from those that have been allocated to the customer. For given total amount of resources employed and the number of applications in the system, the amount of resources released at the completion of service, does not depend on the behavior of the system up to this point and has a distribution function, which can be easily computed using Bayes’ formula. Random processes describing the behavior of simplified systems are easier to analyze, because there is no need to memorize the volume of resources held by each customer. It is enough to record the total amount of occupied resources. The simulation results say that the characteristics of the original and simplified systems are very close.queuing systemslimited resourcesloss probabilitypiecewise linear Markov processсистема массового обслуживанияограниченные ресурсывероятность потери вызовакусочно-линейчатый марковский процесс[Наумов В. А., Самуйлов К. Е., Яркина Н. В. Теория телетрафика мультисервисных сетей. - Москва: РУДН, 2007. - 192 с.][Гнеденко Б. В., Коваленко И. Н. Введение в теорию массового обслуживания. - Москва: Наука, 1966. - 432 с.][Dagpunar J. Principles of Random Variate Generation. - Oxford University Press, 1988. - 248 p.]