Summary: Interarrival and Waiting times
Realization of N(t) (# events in (0, t])
Define:
Sn = time of nth
event = nth
waiting time
Tn = nth
interarrival time = Sn - Sn-1
Distribution of Sn:
Note that Sn t N(t) n, so
P(Sn t) = P(N(t) n)
= 1 -
n-1
k=0
(t)k
e-t
k!
Hence Sn Erlang(n, )
1
Distribution of Tn:

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

Collections: Engineering