Point processes in fast Jackson networks
成果类型：
Article
署名作者：
Martin, JB
署名单位：
Universite PSL; Ecole Normale Superieure (ENS); Inria
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2001
页码：
650-663
关键词：
摘要：
We consider a Jackson-type network, each of whose nodes contains N identical channels with a single server. Upon arriving at a node, a task selects m of the channels at random and joins the shortest of the m queues observed. We fix a collection of channels in the network, and analyze how the queue-length processes at these channels vary as N --> infinity. If the initial conditions converge suitably, the distribution of these processes converges in local variation distance to a limit under which each channel evolves independently. We discuss the limiting processes which arise, and in particular we investigate the point processes of arrivals and departures at a channel when the networks are in equilibrium, for various values of the system parameters.