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SUMMARY:Stability criteria and applications for randomised load balancing 
 schemes - Bramson\, M (Minnesota)
DTSTART:20100422T150000Z
DTEND:20100422T160000Z
UID:TALK24370@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In this takl\, we consider randomised load balancing schemes w
 here an arriving job joins the shortest of $d$ randomly chosen queues from
  among a pool of $n$ queues. Vvekenskaya\, Dobrushin and Karpelevich (1996
 ) considered the case with Poisson imput and exponentially distributed ser
 vice times and derived an explicit formula for the equilibrium distributio
 n for fixed $d$ as $n$ goes to infinity. Since its tail decays doubly expo
 nentially fast\, this distribution is useful in various applications.\n\nR
 elatively little work has been done for general service times or input. Fo
 r general service times\, the behaviour of the service rule at each queue 
 will now play a role in the behaviour of the system. In particular\, the q
 uestion of under which conditions the system is stable (ie\, its underlyig
 n Markov process is positive recurrent) for fixed $n$ is no longer obvious
 . Ideally one would like to understand the limiting behaviour for such equ
 ilibria (provided they exist) as $n$ goes to infinity\, as in the first pa
 ragraph.\n\nHere\, we discuss results that show that for fiex $n$ such sys
 tems are always stable for the appropriate notion of traffic intensity. Th
 ese results also show that the associated equilibria are tight when restri
 cted to a finite number of queues and hence subsequential limits exist as 
 $n$ goes to infinity. It is anticipated that this behaviour will provide a
  general framework for examining the behaviour of such limits under differ
 ence service rules. In this context\, we briefly discuss joint work with Y
  Lu and B Prabhakar on the limiting behaviour of the equilibria when servi
 ce at each queue is given by the standard first-in\, first-out rule.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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