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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