Simulation input analysis: difficulties in simulating queues with Pareto service

Authors:
Donald Gross;John F. Shortle;Martin J. Fischer;Denise M. B. Masi
Affiliations:
George Mason University, Fairfax, VA;George Mason University, Fairfax, VA;Mitretek Systems, Falls Church, VA;Mitretek Systems, Falls Church, VA
Venue:
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Year:
2002

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Abstract

M/G/1 queues, where G is a heavy-tailed distribution, have applications in Internet modeling and modeling for insurance claim risk. The Pareto distribution is a special heavy-tailed distribution called a power-tailed distribution, and has been found to serve as adequate models for many of these situations. However, to get the waiting time distribution, one must resort to numerical methods, e.g., simulation. Many difficulties arise in simulating queues with Pareto service and we investigate why this may be so. Even if we are willing to consider truncated Pareto service, there still can be problems in simulating if the truncation point (maximum service time possible) is too large.