Conditions for a product-form stationary distribution of one queueing system with batch transfers and a disaster flow

We consider an open exponential network with two types of arrival flows at the network nodes: a message flow and a disaster flow. Messages arriving at the nodes form batches of customers of a random size. A disaster arrival at a node completely empties the queue at the node if it is nonempty and has...

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Bibliographic Details
Published in:Problems of information transmission 2014, Vol.50 (1), p.106-116
Main Author: Starovoitov, A. N.
Format: Article
Language:English
Subjects:
Communication Network Theory
Communications Engineering
Control
Electrical Engineering
Engineering
Information Storage and Retrieval
Networks
Systems Theory
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Summary:We consider an open exponential network with two types of arrival flows at the network nodes: a message flow and a disaster flow. Messages arriving at the nodes form batches of customers of a random size. A disaster arrival at a node completely empties the queue at the node if it is nonempty and has no effect otherwise. Customers are served in batches of a random size. After a batch is served at a node, the batch quits the network and, according to a routing matrix, either sends a message or a disaster to another node or does not send anything. We find conditions for the stationary distribution of the network state probabilities to be represented as a product of shifted geometric distributions.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946014010074