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Importance Sampling for Weighted-Serve-the-Longest-Queue

Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
dupuis{at}dam.brown.edu
kevinleder{at}gmail.com
huiwang{at}cfm.brown.edu

This paper considers buffer overflow probabilities for stable queueing systems with one server and different classes of arrivals. The service priority is given to the class of customers whose current weighted queue size is the largest (weighted-serve-the-longest-queue policy). We explicitly identify the exponential decay rate for the rare-event probabilities of interest and construct asymptotically optimal importance-sampling schemes for simulation.

Key Words: importance sampling; Isaacs equation; rare events; simulation; Monte Carlo
History: Received: March 1, 2008; revision received: December 28, 2008;