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)1742910.22363/2312-9735-2017-25-4-350-362Research ArticleA Survey on Queuing Systems with Parallel Servingof CustomersGorbunovaA V<p>Gorbunova A. V. - assistant of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)</p>gorbunova_av@rudn.universityZaryadovI S<p>Zaryadov I. S. - Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Senior Researcher of Institute of Informatics Problems of Federal Research Center “Computer Science and Control” Russian Academy of Sciences</p>zaryadov_is@rudn.universitySamouylovK E<p>Samouylov K. E. - professor, Doctor of Engineering Science, head of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)</p>samuylov_ke@rudn.universitySopinE S<p>Sopin E. S. - Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Senior Researcher of Institute of Informatics Problems of Federal Research Center “Computer Science and Control” Russian Academy of Sciences</p>sopin_es@rudn.universityDepartment of Applied Probability and Informatics Peoples’ Friendship University of Russia (RUDN University)Institute of Informatics Problems Federal Research Center “Computer Science and Control” Russian Academy of Sciences1512201725435036210122017Copyright © 2017, Gorbunova A.V., Zaryadov I.S., Samouylov K.E., Sopin E.S.2017<p>This paper is the ﬁrst in a series of two articles devoted to the review of fork-join (inthe western classiﬁcation) queuing systems or systems with the splitting of incoming queries.This system is a natural model for many other real systems. The article describes the fork-joinqueueing model construction and main characteristics of this model. Special attention is paid tomethods of analysis of the response time of the system. Since the exact expression for the meanresponse time is known only for the case of two servers, the article gives a detailed descriptionof the approach to obtaining an accurate expression of this characteristic. For the case whenthe number of servers is more than two, approximations of the mean response time are obtainedby diﬀerent methods, which is explained by the complexity of the studies due to the existingdependence between the queues of subqueries due to common arrival moments. The paperpresents several methods of approximate analysis: various variants of empirical approximation,i.e. methods that reﬁne the obtained characteristics by using the results of simulation modeling;interpolation methods using system load limit values in cases when the incoming ﬂow and servicetime distributions are not exponential.</p>queuing systemsplitting of requestsparallel service of requestsparallel processingresponse timeсистема массового обслуживаниярасщепление заявокпарал-лельное обслуживание заявокпараллельная обработкавремя отклика[R. Nelson, A. N. Tantawi, Approximate Analysis of Fork/Join Synchronization in Parallel Queues, IEEE Transactions on Computers 37 (1988) 739–743.][Thomasian, Analysis of Fork/Join and Related Queueing Systems, ACM Computing Surveys (CSUR) 47 (2) (2014) 17:1–17:71.][Tsimashenka, W. J. Knottenbelt, Reduction of Subtask Dispersion in Fork-Join Systems, in: Computer Performance Engineering, Springer Berlin Heidelberg, 2013, pp. 325–336.][V. 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