An Introduction to Queueing Theory by U. Narayan Bhat

Author:U. Narayan Bhat
Language: eng
Format: epub
Publisher: Birkhäuser Boston, Boston, MA

7.6 Closed Jackson Networks

Suppose and in the assumptions made while defining the open Jackson network. Let be the total number of customers in the network. Now we have a closed Jackson network, which can be used to model a network of queues with a fixed number of customers.

Following the same reasoning as in open networks with nodes, and the th node supporting servers , the limiting distribution can be obtained in the product form as

(7.6.1)

where

(7.6.2)

and with satisfying the relation

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