Talk:Gordon–Newell theorem

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Conditions?[edit]

The present version of this article, together with Gordon–Newell network, don't give enough conditions for the stationary distribution to be unique ... clearly there could be disjoint subnetworks of queues with stationary distributions within each. Melcombe (talk) 13:43, 27 January 2009 (UTC)[reply]

The distribution is unique. Suppose (as a 'worst case') all the queues were disjoint and thus independent, then the result given is

\scriptstyle {\pi (k_{1},k_{2},\ldots ,k_{m})=\pi (k_{1})\pi (k_{2})\ldots \pi (k_{m}).}

Can you give an explicit example of what you mean? Gareth Jones (talk) 18:41, 9 March 2009 (UTC)[reply]

Enumerative Combinatorics[edit]

I have just removed the text "It turns out that this constant can be evaluated in closed form as well (see, e.g., exercise 7.4 of Stanley, R. P. Enumerative Combinatorics, vol. 2, Cambridge, (1999)), although this is not well known within the queueing theory community." from the article. Exercise 7.4 in the book is very short and states simply "Show that $h_{r}(x_{1},\ldots ,x_{n})=\sum _{k=1}^{n}x_{k}^{n-1-r}\prod _{i\neq k}(x_{k}-x_{i})^{-1}$ ." The contribution was anonymous so I can't follow it up and ask for clarification. Gareth Jones (talk) 17:01, 8 October 2010 (UTC)[reply]