Rare event simulation

Discrete event simulation as a method for performance evaluation has become an indispensable tool in many fields, e.g., teletraffic engineering. New communication networks and services pose extreme requirements regarding the quality of service, e.g., cell loss probabilities in ATM1 networks in the order of 10 . Straightforward simulation for this type of rare event leads to simulation run times in the order of months and years, thus requiring new methods to be investigated and employed. In the following the state of the art in the field of Rare Event Simulation is described and examples are given for the RESTART2/LRE3 method to demonstrate the type of results that can be achieved by using these methods. In recent years these methods have been applied to relevant quality of service parameters in ATM networks. Future applications will concern the investigation of the emerging quality of service concepts for Next Generation Internets. RESTART/LRE is a multi-step simulation approach which reduces the simulation run time by several orders of magnitude from, e.g., years to minutes, thus making simulation studies for rare events feasible. The approach can be applied to single nodes and networks. It is a so-called importance splitting method, where system states that lead to the rare event are saved and used as the starting point for new simulation subruns. The results of the sub-runs are multiplied with the corresponding weights which are obtained in the previous step and result in the desired probabilities. The statistical evaluation method LRE used in this combined approach has the additional advantage of evaluating the socalled local correlation function which gives insight into the correlation {cg,elm,fuss}@comnets.uni-bremen.de, www.comnets.uni-bremen.de [email protected] ATM: Asynchronous Transfer Mode REpetitive Simulation Trials After Reaching Threshold Limited Relative Error structure of the investigated random variable and is part of an error measure for controlling all phases of a simulation. Examples are given for the loss probability of ATM cells in G/G/1/N4 type systems as well as certain tandem networks that represent a model for ATM reference connections. Additional results are presented where the rare event details of the delay time distribution are the object of the investigation. The RESTART/LRE simulation offers as a result the complementary distribution function of the delay time distribution so that the probability of delays longer than a given maximum can be deduced directly from this result. This is one of the quality of service parameters defined for ATM. Furthermore, new results are available where the method has been used to investigate rare event details of the loss probabilities for handover in wireless ATM networks. The underlying model for an ATM reference connection consists of a network with a sequence of */D/1/N 5 queues and an extra delay (propagation and switching) between these queues. Additional traffic is offered to the outgoing connections to model the interference of other ATM connections. Simulation results for the complementary distribution function of the delay time are presented.