Title: A note on integrating products of linear forms over the unit simplex,
Abstract: Integrating a product of linear forms over the unit simplex can be done in
polynomial time if the number of variables n is fixed (V. Baldoni et al.,
2011). In this note, we highlight that this problem is equivalent to obtaining
the normalizing constant of state probabilities for a popular class of Markov
processes used in queueing network theory. In light of this equivalence, we
survey existing computational algorithms developed in queueing theory that can
be used for exact integration. For example, under some regularity conditions,
queueing theory algorithms can exactly integrate a product of linear forms of
total degree N by solving N systems of linear equations.