ECEN4533 Exam
#1 6 March 2006
1) A 12 Mbps RedNeckNet backbone trunk is carrying a mix of data and
voice traffic. The voice traffic is known to have exponentially
distributed interarrival times (IAT) and packet size, with means
of 410 micro seconds and 61 bytes respectively. The data traffic
is also know to have exponentially distributed IAT and packet sizes,
with means of 930 micro seconds and 603 bytes respectively.
Suppose RedNeckNet implements DiffServ and tags voice traffic as high
priority and data traffic as low priority.
[15] What does classical queuing theory predict will be the mean time a
high priority packet will spend in the switch? [Answer = 238.0 micro seconds]
[10] What does classical queuing theory predict will be the mean time a
low priority packet will spend in the switch? [823.1 micro seconds]
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2) A packet switch has a 12 Mbps output trunk that is running at a 53 %
load. The average packet size is 226.8 bytes. Assuming that
the system can be modeled as an M/M/1 queue...
[15] Compute the average time a packet spends in the switch. [321.7 micro seconds. Note
that 53% is the overall load for problem 1, and 226.8 bytes is the
average packet size for problem 1. Hence this is the result that
would occur if problem 1's traffic was handled by a FIFO queue.]
[10] Compute the probability there are exactly 3 packets in the
switch. [0.06977]
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3) You are estimating the required buffer size for a packet switch that
needs to be able to store 10,000 packets. Packets to be stored
are known to be statistically independent and to have an exponentially
distributed size with a mean of 690 bytes. Define the random
variable Xi to be the number of bytes in the ith packet being stored,
and let the random variable Y = X1 + X2 + ... + X9999 + X10000 be the
number of bytes required to store 10,000 randomly chosen packets.
Knowing that when statistically independent random numbers are added
together, the result (Y) is Gaussian Distributed with a mean and
variance 10,000 times larger than the mean and variance of a single
packet (i.e. E[Y] = 10000E[X] and σ2Y = 10000σ2X)...
[10] Compute the variance of the random variable Y. [4.761*109 bytes2]
[15] Compute the actual buffer size required if you desire, with a 99%
probability, to have sufficient memory to store 10,000 packets. [Need at least 7.061 MB]
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4) Suppose TCP has successfully opened a logical link to a destination,
and now needs to send one packet over that logical link. The
normal procedure would be to: (1) Transmit the
packet, start a timeout timer, and wait for an acknowledgement (ACK).
(2) Upon receiving the packet, the receiver will
immediately send an ACK.
(3) Upon receiving the ACK, the transmitter
considers that the packet has been successfully transmitted.
If an ACK is not received by the transmitter within
the timeout period, the transmitter will go back to step (1).
Assume that the transmitter will attempt a total of 3 transmissions
(the original plus 2 retransmissions) before giving up and posting a
"Connection Lost" message on the user's monitor, and that uncorrupted
ACK's arrive back at the transmitter well before the timeout period
expires. Also assume that the system is very noisy such that P(a
message packet is discarded) = P(an ACK is discarded) = 0.58.
[15] Compute the P(the transmitter fails to receive an ACK from the 1st
transmission). [0.8236]
[10] Compute the P(the transmitter fails to receive an ACK from all
three transmissions).
[0.5587]
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