Publisher： Cambridge University Press
E-ISSN： 1475-6064|46|1|76-101
ISSN： 0001-8678
Source： Advances in Applied Probability, Vol.46, Iss.1, 2014-03, pp. : 76-101
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage to the fluid dynamics, the server switches between the queues infinitely many times in any finite time interval causing frequent oscillatory behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid limit is random. In addition, we suggest a method that establishes finiteness of moments of the busy period in an M/G/1 queue.
Related content
Ratio Limit Theorems for Random Walks and Lévy Processes
Potential Analysis, Vol. 23, Iss. 4, 2005-12 ,pp. :
Access to resources
Recommend
Limit laws on extremes of nonhomogeneous Gaussian random fields
Journal of Applied Probability, Vol. 54, Iss. 3, 2017-09 ,pp. :