(a)

Compute probability the wait time for a Bundle is at most 1 hr:


(b)

Erlang distribution:

Desired probability:

This integral requires iterated IBP.


(c)

The results disagree. Method 2 is the correct approach assuming individual calls arrive according to a Poisson process.

It turns out that if you have some Poisson process, bundles of arrivals do not themselves follow a Poisson process.

Think of a Poisson process as some dots scattered on a timeline. Place a heavy dot at the location of each dot in order, and erase all other dots. These heavy dots do not follow a Poisson process.