Fast Simulation of Networks of Queues with Effective and Decoupling Bandwidths

A significant difficulty when using Monte Carlo simulation for the performance analysis of communication networks is the long runtime required to obtain accurate statistical estimates. Under the proper conditions, importance sampling (IS) is a technique that can speed up simulations involving rare events in network (queueing) systems. Large speed-up factors in simulation runtime can be obtained with IS if the modification or bias of the underlying probability measures of certain random processes is carefully chosen. Fast simulation methods based on large deviation theory (LDT) have been successfully applied in many cases. In this paper, we set up an IS-based simulation of various elementary network topologies. These configurations are frequently encountered in broadband ATM-based network components such as switches and multiplexers. Our objective in this study is to obtain the optimal or near-optimal biasing parameter values of the arrival processes for the importance sampling simulation. For this purpose we appropriately apply a technique presented by Chang et al. for certain portions of the networks (intree) while we develop a new algorithm, inspired by the work of De Veciana et al. on decoupling bandwidths, for the non-intree portion of the network.

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