NDLI: Marginal queue length approximations for a two-layered network with correlated queues

Content Provider	Springer Nature Link
Author	Boxma, O. J. Dorsman, J. L. Vlasiou, M.
Copyright Year	2013
Abstract	We consider an extension of the classical machine-repair model, where we assume that the machines, apart from receiving service from the repairman, also serve queues of products. The extended model can be viewed as a layered queueing network, where the first layer consists of the queues of products and the second layer is the ordinary machine-repair model. As the repair time of one machine may affect the time the other machine is not able to process products, the downtimes of the machines are correlated. This correlation leads to dependence between the queues of products in the first layer. Analysis of these queue length distributions is hard, as the exact dependence structure for the downtimes, or the queue lengths, is not known. Therefore, we obtain an approximation for the complete marginal queue length distribution of any queue in the first layer, by viewing such a queue as a single server queue with correlated server downtimes. Under an explicit assumption on the form of the downtime dependence, we obtain exact results for the queue length distribution for that single server queue. We use these exact results to approximate the machine-repair model. We do so by computing the downtime correlation for the latter model and by subsequently using this information to fine-tune the parameters we introduced to the single server queue. As a result, we immediately obtain an approximation for the queue length distributions of products in the machine-repair model, which we show to be highly accurate by extensive numerical experiments.
Ending Page	63
Page Count	35
Starting Page	29
File Format	PDF
ISSN	02570130
e-ISSN	15729443
Journal	Queueing Systems
Issue Number	1
Volume Number	75
Language	English
Publisher	Springer US
Publisher Date	2013-01-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Queues and service Systems Theory, Control Performance evaluation; queueing; scheduling Operations Research/Decision Theory Machine-repair model Production/Logistics/Supply Chain Probability Theory and Stochastic Processes Layered queueing networks Queues with server vacations Queueing theory Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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