ECEN4533 Exam
#2 13 April 2005
1) A packet switch is to be used to move compressed variable rate 32
Kbps voice traffic. Packets must clear this switch within 60 msec
of generation, on average, to meet end-to-end delivery targets.
250 byte packets are being used, of which 200 bytes are voice and 50
bytes are overhead. These packets require 50 msec to assemble,
leaving only 10 msec, on average, for the traffic to spend in the
packet switch in question. Given a trunk speed of 1.2 Mbps, and
assuming that the packet inter-arrival times and sizes are both
exponentially distributed...
[10] Compute the trunk load that can be placed on the switch. [Answer: 0.8333]
[15] Compute the number of voice calls the system can support. [Answer: 25]
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2) The traffic, X, on a particular trunk line is Gaussian Distributed
with a mean of 990 Kbps, and a standard deviation of 100 Kbps.
[10] Compute the P( X > 1,060 Kbps). [Q(0.7) = 0.2420]
[15] Suppose you're trying to estimate this load, and you take two
statistically independent samples, X1 and X2, in order to calculate a
sample mean Y = (X1 + X2)/2. Compute P( Y > 1,060 Kbps).
[Q(0.99) = 0.1611]
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3) A server is downloading a file to a client and is using sliding
window control and the Go-Back-N ARQ protocol. The server
has a window size of 4 and is communicating with the client over a link
with a normalized propagation delay of 4. 7 full sized packets
must be delivered in order to download this file. The time to
inject one packet into this network is 80 msec. ACK's are
generated by the client immediately upon receipt of a packet, and
acknowledge the packet just received and any received correctly
beforehand. Suppose packet #1 disappears en route from the client
to the server. The server has a TIME OUT value of 1 second (clock
starts when the trailing edge of a packet is injected into the link by
the server and stops when the trailing edge of the ACK for that packet
is received by the server).
[10] Compute the one-way propagation delay, in seconds, for this
system. [320 msec]
[15] Compute the time it takes for the file to be completely delivered
to the client. The clock starts when the server transmits the
leading edge of packet #1, and stops when the client receives the
trailing edge of packet #7. Assume any logical links have
already been opened. For the purpose of this problem, assume
ACK's are the same size as the packets. [2.440 seconds]
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4) A packet switch is connected to a 340 Kbps trunk line, with an 88%
load. The average packet size is 250 bytes, and the system has
self-similar traffic with an H parameter of 0.95.
[10] Compute the average number of packets in the switch. [8.717*1016]
[10] Compute the average time a packet spends in the switch. [5.827*1014 seconds = 1.848*107 years]
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