2010/06/29 by Tan, Sen, Xia, Aihua
#60E15 #FOS: Mathematics #Primary 60G55 #Probability (math.PR) #secondary 60F05
paper · doi:10.48550/arxiv.1006.5545
Melamed's theorem states that for a Jackson queuing network, the equilibrium flow along a link follows Poisson distribution if and only if no customers can travel along the link more than once. Barbour & 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 paper, we prove that the customer flow process is a Poisson cluster process and then establish a general approximate version of Melamed's theorem accommodating all possible cases of 0≤ p<1.