A two-queue polling model with priority on one queue and heavy-tailed On/Off sources: a heavy-traffic limit

Rosario Delgado ()
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Rosario Delgado: Universitat Autònoma de Barcelona

Queueing Systems: Theory and Applications, 2016, vol. 83, issue 1, No 4, 57-85

Abstract: Abstract We consider a single-server polling system consisting of two queues of fluid with arrival process generated by a big number of heavy-tailed On/Off sources, and application in road traffic and communication systems. Class-j fluid is assigned to queue j, $$j=1,2$$ j = 1 , 2 . Server 2 visits both queues to process or let pass the corresponding fluid class. If there is class-2 fluid in the system, it is processed by server 2 until the queue is empty, and only then server 2 visits queue 1, revisiting queue 2 and restarting the cycle as soon as new class-2 fluid arrives, with zero switchover times. Server 1 is an “extra” server which continuously processes class-1 fluid (if there is any). During the visits of server 2 to queue 1, class-1 fluid is simultaneously processed by both servers (possibly at different speeds). We prove a heavy-traffic limit theorem for a suitable workload process associated with this model. Our limit process is a two-dimensional reflected fractional Brownian motion living in a convex polyhedron. A key ingredient in the proof is a version of the Invariance Principle of Semimartingale reflecting Brownian motions which, in turn, is also proved.

Keywords: Polling model; Reflected fractional Brownian motion; Convex polyhedron; On/Off sources; Workload process; Heavy-traffic limit; Skorokhod problem; 60K25; 60F05; 60G15; 60G18; 60G22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11134-016-9479-9

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