1
Purdue University
ECE
ECE-
547
547
Introduction to Computer
Introduction to Computer
Communication Networks
Communication Networks
Instructor:
Instructor:
Xiaojun
Xiaojun
Lin
Lin
Lecture 9
Lecture 9
Purdue University
Superposition of Poisson
Superposition of Poisson
¾
Theorem:
Let {L
t
, t
≥
0} and
{M
t
, t
≥
0}
be two
independent
Poisson
Processes with rates
λ
and
μ
, respectively.
For each
ω∈Ω
and t
≥
0,
let
N
t
(
ω
) = L
t
(
ω
) + M
t
(
ω
)
Then the resulting process {N
t
, t
≥
0} is called the superposition
of processes
{L
t
, t
≥
0} and
{M
t
, t
≥
0} and is a Poisson Process
with rate
λ
+
μ
.
L
t
M
t
N
t

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