Information Streams
and Traffic Processes
Professor Izhak Rubin
Electrical Engineering Department
UCLA
© 2010-2011 by Izhak Rubin

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(c) Prof. Izhak Rubin
2
Arrival Point Processes (1)
z
Messages arrive at the system in accordance with a
stochastic point
process
:
where A
n
denotes the arrival time of n
th
message, n
≥
1. We generally
set A
0
=0.
z
Associated with the arrival process A is the
arrival counting
process
.
where N
t
≡
N(t) denotes the arrival count at t, expressing the number
of messages arriving at the system during (0, t].
{
}
(1)
,
1
.
.
,
1
,
1
p
w
A
A
n
A
A
n
n
n
>
≥
=
+
{
}
(2)
,
0
,
0
,
0
=
≥
=
N
t
N
N
t
N(t)
t
A
0
A
1
A
2
A
3
1
2
0
T
2
T
3
T
1