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SUMMARY:Proportional Fairness and its Relationship to Multi-class Queueing
  Networks - Neil Walton (Statslab)
DTSTART:20080721T113000Z
DTEND:20080721T120000Z
UID:TALK12908@talks.cam.ac.uk
CONTACT:James Cruise
DESCRIPTION:\nA network of single server queues with routing is considered
 . It is proven a sequence of such networks can converge weakly to a stocha
 stic flow level model. A large deviations principle for the stationary dis
 tribution of these networks is found. Its rate function has a dual formula
 tion that coincides with proportional fairness. It is proven the throughpu
 t of the original queueing model behaves as a proportionally fair allocati
 on as the number of customers across routes increases.\n\nThe queueing net
 works considered have no prescribed optimization structure. Regardless of 
 this\, we find proportional fairness forms the entropy minimizing state of
  these networks. From this it is found proportionally fair optimization oc
 curs as a consequence of state space collapse behaviour in these non-optim
 izing queueing models.\n\nThis work merges classical results on queueing n
 etworks and recent work on proportional fairness. One could view these see
 mingly different models as the same system described at different levels o
 f granularity: a microscopic packet/queueing level description\; a macrosc
 opic flow level description and a teleological optimization description. 
LOCATION:MR3\, CMS
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