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Interarrival and Waiting times Realization of N(t) (# events in (0, t])
 

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