# We have shown that if two independent Poisson streams are merged, we still get a Poisson stream. Now

- September 24, 2021 /
- ecommerce Development, web development, Software Development, Online marketing, Magento, Ecommerce

We have shown that if two independent Poisson streams are

merged, we still get a Poisson stream. Now consider two independent renewal

counting processes N1(t) and N2(t) being merged into the process N(t) [SEVC

1977]. Let the underlying distribution functions be FX1 , FX2 , and FX. First

show that, conditioned on the fact that the last event in the output stream was

contributed by the first stream, the time to next event in the output stream is

the minimum of X1 and Y2 = Y (X2), where Y (X2) is the residual time to next

event in input stream 2. Next show that x