Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On customer flows in Jackson queuing networks   Melamed's theorem states that for a Jackson queuing network, the equilibrium
flow along a link follows Poisson distribution if and only if no customers can
travel along the link more than once. Barbour \& Brown~(1996) considered the
Poisson approximate version of Melamed's theorem by allowing the customers a
small probability $p$ of travelling along the link more than once. In this
paper, we prove that the customer flow process is a Poisson cluster process and
then establish a general approximate version of Melamed's theorem accommodating
all possible cases of $0\le p<1$.

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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio