It is named after the authors of the paper where the network was first described: Baskett, Chandy, Muntz, and Palacios.
[1] The paper is well known, and the theorem was described in 1990 as "one of the seminal achievements in queueing theory in the last 20 years" by J. Michael Harrison and Ruth J.
For a BCMP network of m queues which is open, closed or mixed in which each queue is of type 1, 2, 3 or 4, the equilibrium state probabilities are given by where C is a normalizing constant chosen to make the equilibrium state probabilities sum to 1 and
The original proof of the theorem was given by checking the independent balance equations were satisfied.
Peter G. Harrison offered an alternative proof[4] by considering reversed processes.