Simulating Poisson process/Random numbers

Hi,

I have a model which uses the exponential distribution to estimate
inter-arrival times of events from various sources. This estimation or
prediction assumes that the inter-arrival times from the various event
sources combine to form an exponential distribution, or that the
combination of sources can be modelled as a poisson process.

To test the model I'm trying to determine how to generate random
inter-arrival times from multiple sources such that the combined
distribution of their inter-arrival times forms an exponential
distribution. The central limit theorem only applies to normal
distributions, therefore if I generate random inter-arrival times at
each source using an exponential distribution with different mean the
combined distribution will not be exponential.


If I generate the inter-arrival times at each source using the same
exponential distribution, with the same mean, then the resulting
distribution should be the same original exponential distribution.
However, I want some way of varying the mean inter-arrival time of each
source but still have a resulting combined distribution which is
exponential.



Is this possible??

Thanks

-Mike

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