Comments on duality of queues with finite buffer size
type: Item
instance of: scholarly article
title: Comments on duality of queues with finite buffer size
zbMATH Open document ID: 0797.60077
DOI: 10.1016/0167-6377(93)90016-A
author: V. Pereyra
published in: Operations Research Letters
publication date: 1994-10-10T00:00:00Z
review text: The issue of duality of queues has been studied by several authors, however, only for the infinite-buffer case. For finite buffer queueing systems, the developed duality principles are less useful. Therefore the concept of quasi-duality is introduced. Quasi-duality is defined, rather informally, in such a way that the \(G1/G2/1/K\) and the \(G2/G1/1/K\) queueing systems are quasi-dual, if the role of customers and non- customers, i.e., empty buffer spots, are reversed. Important to note here is that the above two queueing systems are not ``normal'' duals; they only behave the same if they are neither empty nor totally full. For some specific cases, i.e. the \(M/M/1/K\), the \(E2/M/1/K\) and the \(M/D/1/K\) queueing systems, the quasi-duals are discussed.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 527407
zbMATH Keywords: duality of queues
zbMATH Keywords: infinite buffer
zbMATH Keywords: quasi-duality
reviewed by: B. R. Haverkort
MaRDI profile type: Publication
cites work: Q5624436
cites work: Q3855869
cites work: Q4101255
cites work: Duality and Other Results for M/G/1 and GI/M/1 Queues, Via a New Ballot Theorem
cites work: A duality relation for busy cycles in GI/G/1 queues
cites work: Q5339835
description: scientific article; zbMATH DE number 527407