## Homework 5 (due at beginning of class on Nov. 19, 2014, Wed)

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PROBLEM 1  (10 points)

Consider the 5-bit generator, G=10011, and suppose that D has the
value 1010101010.  What is the value of R?

PROBLEM 2

Consider the slotted ALOHA protocol as analyzed in
lecture slide 5-18.  The channel is time slotted.
Each packet transmission fits exactly into a time slot.
Suppose N=3.  That is, there are three stations attempting
to transmit into every time slot with probability P.
For a particular time slot,

i.  what is the probability that it is empty?      (3 points)

ii. what is the probability that it has exactly one
packet transmission?                           (3 points)

iii.  what is the probability that it has a collision, i.e.,
two or more packets transmitted in it?       (3 points)

iv. calculate the probability in part ii for
P equal to 0.2, 0.3, and 0.4.                  (6 points)

PROBLEM 3

Consider the channel efficiency formula for the CSMA/CD
protocol in lecture slide 5-28, where the numerical value
of e is 2.72, t_prop is the maximum channel propagation time,
and t_trans is the transmission time of a 1500-byte packet.

Consider an Ethernet where the maximum cable distance between any two
stations is 1000 meters.  The signal propagation speed in the cable is
2x10**8 meters/second.

i.  Calculate t_prop.                                        (3 points)

ii.  Calculate t_trans for each of three different transmission rates:
10 Mbps, 100 Mbps, and 1 Gbps.                          (6 points)

iii.  Calculate the CSMA/CD channel efficiency for each of the three
transmission rates:  10 Mbps, 100 Mbps, and 1 Gbps.    (6 points)

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