By Eugen Lamers
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Extra resources for Contributions to Simulation Speed-Up
The intervals between the thresholds and the limits are called steps and match the importance regions. 1) PB|I ≥ PB Generally, on its path from the starting state at x = 0 to the rare event of interest B, the stochastic process has to visit the intermediate states, including the threshold I . This leads to the relation P0 > PI > PB . Further, this is why it can be expected to reach the rare event faster from an intermediate state like the threshold I than from the starting state or other states below I .
Further discussion on the topic, whether there can be jumps over one or more thresholds and the impact on the efﬁciency, can be found in [Gar00] and [VA98]. 3 Procedure To enable the favouring of importance regions, the simulation must stop at the time when a transition from the current step to the next lower step is performed. Steps represent the important regions and are called steps since they are ordered. At that transition, the simulation has to restart with a trace which tends to go up again in order to remain in the current importance region and to approach values closer to the rare event of interest.
For the node this is straightforward, since the information about the queue occupancy is available to the node. If parameters from more than one node need to be collected for the IF, e. , the sum of the occupancies of node A and node B, one node still must be responsible for the decision about the discrete times when the values are collected and used for the IF. Such times can be the events of arrivals to that node. Two approaches to collect the parameters from all involved nodes are considered.
Contributions to Simulation Speed-Up by Eugen Lamers