A method of approximate analysis of an open exponential queuing network with losses due to finite shared buffers in multi-queue nodes

Miron Vinarskiy

European Journal of Operational Research, 2017, vol. 258, issue 1, 207-215

Abstract: We consider a model of an open exponential queuing network where each node comprises several multi-class MR/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.

Keywords: Queuing; Queuing network; Multi-queue node; Finite buffer; Losses (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221716307834
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:258:y:2017:i:1:p:207-215

DOI: 10.1016/j.ejor.2016.09.031

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().