Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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.
['Thomas Bonald', 'Minh-Anh Tran']
I am writing a research paper on a idea On Kelly networks with shuffling
[{"from": "human", "value": "I am writing a research paper on a idea On Kelly networks with shuffling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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.  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."}]