On customer flows in Jackson queueing networks
Melamed's theorem states that, for a Jackson queueing network, the equilibrium flow along a link follows a Poisson distribution if and only if no customers can travel along the link more than once. Barbour and 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 note, we prove that the customer flow process is a Poisson cluster process and then establish a general approximate version of Melamed's theorem that accommodates all possible cases of 0 ≤ p < 1.
Permanent link to this document: http://projecteuclid.org/euclid.aap/1293113152
Digital Object Identifier: doi:10.1239/aap/1293113152
Zentralblatt MATH identifier: 05848652
Mathematical Reviews number (MathSciNet): MR2796678