1)
a)
Suppose the number of sharing stations is N, the probability that a station has a
packet to transmit in one packet time is p. A transmission is successful only when
there is one station transmits at the current slot and no more station will transmit
in the next slot. Therefore, the successful transmission probability is:
2(
1)
98
(1
)
50*0.98 *0.02
0.138
N
N
p
p


=
=
If there is some packet to be transmitted, the successful transmission probability is
the conditional probability that no other packets arrives when one packet has to be
sent out, thus the successful transmission probability is:
2(
1)
98
(1
)
0.98
0.138
N
p


=
=
b)
Suppose the link capacity is C, the packet length is L, when there is no collision,
system capacity in terms of packet is:
2
2000
/ sec
1000
packet
Mbps
C
C
packets
L
bits
=
=
=
Hence, in one minuet, successfully transmitted packet is:
* *60sec
2000*0.138*60
16560
packet
C
p
packets
=
=
2)
a)
We can represent the message as:
9
8
7
5
3
2
x
x
x
x
x
x
+
+
+
+
+
and
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 Spring '11
 Prof.ShenghuiSong
 Conditional Probability, Units of information, Byte

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