A semi-product-form for the equilibrium state probabilities in a pair of queues with finite batches
File(s)
Published version
Author(s)
Harrison, PG
Type
Conference Paper
Abstract
A Markovian network of two queues, with finite size batch Poissonarrivals and departures, is solved approximately, but to arbitraryaccuracy, for its equilibrium state probabilities. Below a pair ofthresholds on the queue lengths, a modification of the SpectralExpansion Method is used to construct a semi-product-form at alllengths of one queue in a finite lattice strip defined by the thresh-old of the other queue. No additional special arrival streams arerequired, for example at empty queues, from which it is alreadyknown that a product-form can be constructed. Hence the firstexact closed form solution for the equilibrium probabilities in anunmodified Markovian queueing network with batches is obtained,the only constraint being finiteness of the batches. The methodis illustrated numerically, first in a tandem network and then in atwo-node network with feedback. Simulation results confirm theprecision of the method, lying almost on top of the those of themodel in plots. Partial batch forwarding and discarding are therebycompared quantitatively.
Date Issued
2019-03-01
Date Acceptance
2018-12-22
Citation
2019, pp.31-38
Publisher
ACM
Start Page
31
End Page
38
Copyright Statement
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM
Identifier
https://dl.acm.org/doi/10.1145/3306309.3306316
Source
VALUETOOLS 2019
Subjects
Science & Technology
Technology
Computer Science, Theory & Methods
Telecommunications
Computer Science
Queues
product-form
spectral expansion
generating functions
NETWORKS
Publication Status
Published
Start Date
2019-03-13
Finish Date
2019-03-15
Coverage Spatial
Palma de Mallorca, Spain
Date Publish Online
2019-03-01