IEOR announces the following seminar. The details are as follows:
Title: The Concert Queuing Game: To Wait or To be Late
Speaker: Prof. Sandeep Juneja, TIFR, Bombay
Venue: Room 217, Mechanincal Engineering Building,
Time and Date: 11.30AM, 4th November, 2010.
Abstract: We introduce the concert (or cafeteria) queueing problem: A finite but large number of customers arrive into a queueing system that starts service at a specified opening time. Each customer is free to choose her 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 completion time, with coefficients that may be class dependent. We analyze the system in the many-customer asymptotic regime and develop a fluid limit for the resulting queueing system. We consider a fluid model of this system, 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 closing time where all customers are served. Furthermore, the waiting queue is maximal at the opening time, and monotonically decreases thereafter. In the 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 bounds on the PoA. In addition, we consider several mechanisms that may be used to reduce the PoA. We also discuss Nash equilibrium in the single class finite customer setting and show its convergence to the fluid limit equilibrium. The proposed model may explain queueing phenomena in diverse settings that involve a pre-assigned opening time.
All interested are welcome.