A method of approximate analysis of an open exponential queuing network with losses due to finite shared buffers in multi-queue nodes
| Autor: | Miron Vinarskiy |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
Queueing theory 021103 operations research Information Systems and Management General Computer Science Computer science Iterative method Node (networking) 0211 other engineering and technologies Fair queuing 0102 computer and information sciences 02 engineering and technology Management Science and Operations Research Topology 01 natural sciences Industrial and Manufacturing Engineering 010201 computation theory & mathematics Modeling and Simulation Queuing delay Class-based queueing Queue |
| Zdroj: | European Journal of Operational Research. 258:207-215 |
| ISSN: | 0377-2217 |
| DOI: | 10.1016/j.ejor.2016.09.031 |
| Popis: | We consider a model of an open exponential queuing network where each node comprises several multi-class M R / M /1 queues that share a common waiting space (a buffer) of limited capacity. A customer arriving to a node with fully occupied buffer is lost. An assumption is made that each class input traffic to a node, which is a superposition of the class external Poisson flow and the class flows coming from other nodes, is a Poisson process. Under this assumption a method of an approximate analysis is presented. It is based on solving iteratively a system of non-linear equations for the unknown nodal flow rates. It is shown that the gradient iterations solve the multi-class network equations. For the single-class model we use the direct substitution iterations. In the latter case existence and uniqueness of the solution, obtained by the iterative algorithm, is rigorously proven. It is demonstrated for a few network configurations that the network and node performance characteristics received by analytic approach are close to those obtained by simulation method. Our contribution is a performance evaluation methodology that could be usefully employed in queuing network design. |
| Databáze: | OpenAIRE |
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