A symbolic computation approach to a problem involving multivariate Poisson distributions

Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing Wilf–Zeilberger theory and associated algorithms. A symbolic computation package has been developed and is made freely available. A discussion of motivating biomolecular problems is also provided.