On Kelly networks with shuffling

We consider Kelly networks with shuffling of customers within each queue. Specifically, each arrival, departure or movement of a customer from one queue to another triggers a shuffle of the other customers at each queue. The shuffle distribution may depend on the network state and on the customer th...

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Bibliographic Details
Published inQueueing systems Vol. 59; no. 1; pp. 53 - 61
Main Authors Bonald, T., Tran, M.-A.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2008
Springer Nature B.V
Springer Verlag
Subjects
Business and Management
Computer Communication Networks
Computer Science
Control
Customer services
Mathematics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Queuing
Studies
Supply Chain Management
Systems Theory
60J75
Product form
Insensitivity
Symmetric queues
Shuffling
shuffling
symmetric queues
insensitivity
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Summary:We consider Kelly networks with shuffling of customers within each queue. Specifically, each arrival, departure or movement of a customer from one queue to another triggers a shuffle of the other customers at each queue. The shuffle distribution may depend on the network state and on the customer that triggers the shuffle. We prove that the stationary distribution of the network state remains the same as without shuffling. In particular, Kelly networks with shuffling have the product form. Moreover, the insensitivity property is preserved for symmetric queues.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-008-9075-8