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SUMMARY:The concert queueing game: to wait or to be late - Juneja\, S (Tat
 a Institute)
DTSTART:20100616T140000Z
DTEND:20100616T150000Z
UID:TALK25208@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We introduce the concert (or cafeteria) queueing problem: A fi
 nite but large number of customers arrive into a queueing system that star
 ts service at a specified opening time. Each customer is free to choose he
 r arrival time (before or after opening time)\, and is interested in early
  service completion with minimal wait. These goals are captured by a cost 
 function which is additive and linear in the waiting time and service comp
 letion time\, with coefficients that may be class dependent. We analyze th
 e system in the many-customer asymptotic regime and develop a fluid limit 
 for the resulting queueing system. We consider a fluid model of this syste
 m\, which is motivated as the fluid-scale limit of the stochastic system. 
 In the fluid setting\, we explicitly identify the unique Nash-equilibrium 
 arrival profile for each class of customers. Our structural results imply 
 that\, in equilibrium\, the arrival rate is increasing up until the closin
 g time where all customers are served. Furthermore\, the waiting queue is 
 maximal at the opening time\, and monotonically decreases thereafter. In t
 he simple single class setting\, we show that the price of anarchy (PoA\, 
 the efficiency loss relative to the socially optimal solution) is exactly 
 two\, while in the multi-class setting we develop tight upper and lower bo
 unds on the PoA. In addition\, we consider several mechanisms that may be 
 used to reduce the PoA. The proposed model may explain queueing phenomena 
 in diverse settings that involve a pre-assigned opening time.
LOCATION:Seminar Room 1\, Newton Institute
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