Известия Томского политехнического университета: Инжиниринг георесурсов (May 2019)
Using parallel computing in queueing network simulation
Abstract
Queueing networks models are one of the most popular tools of mathematical modeling of various physical systems: telecommunication networks, distributed data processing systems, transportation networks, network models of cash flows, etc. Unfortunately, analytical results of the study of such models can be obtained only in some rather special cases. Therefore, the objectives of the analysis of queueing networks with complex configurations are usually resolved through mechanism of the simulation. However, the main difference of the queueing networks from simple queueing models is that each network can contain many service nodes and these nodes interact with each other. Thus, the simulation of the queueing networks increases the dimension of the tasks executed on one computing device. So, desktop computers cannot perform the required simulation in adequate time. Hence, we have the urgent task of applying the mechanisms of parallel computing and performing simulations using supercomputer clusters. The main aim of the study is to develop and implement the object model of the simulation system of the queueing networks and implement as well the capabilities of parallel computing and statistical processing in order to perform simulation of queueing networks on supercomputer clusters The methods used in the study: simulation based on the discrete/event approach; mathematical models of the event flows, such as Poisson, renewal, Markovian Arrival Process, and semi-Markov processes; statistics data processing; object-oriented methods of analysis, software design and programming, MPI technology. The results. The paper introduces the object model of the software for simulating queueing networks. The application developed on its basis allows simulating queueing networks with rather arbitrary configuration. The parallel computing was implemented and the data were processed. The authors have carried out the real numerical experiments of application execution on the supercomputer cluster of TPU for different dimensions of the task which demonstrated high efficiency of applying parallel computing for simulation of the queueing networks.
