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@inproceedings{Harrison:2019:10.1145/3306309.3306316,
author = {Harrison, PG},
doi = {10.1145/3306309.3306316},
pages = {31--38},
publisher = {ACM},
title = {A semi-product-form for the equilibrium state probabilities in a pair of queues with finite batches},
url = {http://dx.doi.org/10.1145/3306309.3306316},
year = {2019}
}

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TY  - CPAPER
AB  - 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.
AU  - Harrison,PG
DO  - 10.1145/3306309.3306316
EP  - 38
PB  - ACM
PY  - 2019///
SP  - 31
TI  - A semi-product-form for the equilibrium state probabilities in a pair of queues with finite batches
UR  - http://dx.doi.org/10.1145/3306309.3306316
UR  - https://dl.acm.org/doi/10.1145/3306309.3306316
UR  - http://hdl.handle.net/10044/1/66955
ER  -

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