Mean waiting time due to aggregation of k poisson arrivals

#1
Dear Experts: I want to calculate the mean waiting time due to aggregation of k arrivals following poisson process with rate #λ#. Arrivals are served in chunk i.e., if N arrivals reach buffer, OR deterministic timer T expires. The timer ALWAYS starts at the first arrival. So, first arrival reach always at t=0. Can some one explain me how to find the mean waiting time due to k arrivals? Many thanks.
Hint: can we use some kind of uniform distribution of the waiting times of the successive arrivals?
 

Dragan

Super Moderator
#2
Hint: can we use some kind of uniform distribution of the waiting times of the successive arrivals?[/QUOTE said:
I would suggest using an exponential (continuous - waiting time) distribution - given it's well known relationship with the Poisson (discrete) distribution.