regenerative_simulation - Estimation Techniques 131...

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Estimation Techniques 131 Alternatively, we can run one very long simulation. Allow first the simulation to reach its steady state, and then collect the first sample of observations. Subsequently, instead of terminating the simulation and starting all over again, we extend the simulation run in order to collect the second sample of observations, then the third sample and so on. The advantage of this method is that it does not require the simulation to go through a transient period for each sampling period. However, some of the observations that will be collected at the beginning of a sampling period will be correlated with observations that will be collected towards the end of the previous sampling period. The replication method appears to be similar to the batch means approach. However, in the batch means method, the batch size is relatively small and, in general, one collects a large number of batches. In the above case, each sampling period is very large and one collects only a few samples. d. Regenerative method The last two methods described above can be used to obtain independent or approximately independent sequences of observations. The method of independent replications generates independent sequences through independent runs. The batch means method generates approximately independent sequences by breaking up the output generated in one run into successive subsequences which are approximately independent. The regenerative method produces independent subsequences from a single run. Its applicability, however, is limited to cases which exhibit a particular probabilistic behaviour. Let us consider a single server queue. Let t 0 , t 1 , t 2 ,... be points at which the simulation model enters the state where the system is empty. Such time instances occur when a customer departs and leaves an empty system behind. Let t 0 be the instance when the simulation run starts assuming an empty system. The first customer that will arrive will see an empty system. During its service, other customers may arive thus forming a queue. Let t 1 be the point at which the last customer departs and leaves an empty system.
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regenerative_simulation - Estimation Techniques 131...

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