Random Fluid Limit of an Overloaded Polling Model. (March 2014)

• Record Type: Journal Article
• Authors: Remerova, Maria; Foss, Sergey; Zwart, Bert
• Is Part Of: Advances in applied probability. Volume 46:Number 1(2014)
• Page Start: 76
• Page End: 101
• Publication Date: 2014-03
• Subjects: Cyclic polling, -- overload, -- random fluid limit, -- branching process, -- multi-stage gated discipline, -- busy period moment; 60K25, -- 60F17, -- 90B15, -- 90B22; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1239/aap/1396360104
• Languages: English
• ISSNs: 0001-8678

Abstract

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.