Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Max-plus algebra models of queueing networks   A class of queueing networks which may have an arbitrary topology, and
consist of single-server fork-join nodes with both infinite and finite buffers
is examined to derive a representation of the network dynamics in terms of
max-plus algebra. For the networks, we present a common dynamic state equation
which relates the departure epochs of customers from the network nodes in an
explicit vector form determined by a state transition matrix. It is shown how
the matrices inherent in particular networks may be calculated from the service
times of customers. Since, in general, an explicit dynamic equation may not
exist for a network, related existence conditions are established in terms of
the network topology.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio