E&CE 710: Assignment #2
Prof. X. Shen
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Office: EIT 4155
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Prof. X. Shen E&CE 710 : Assignment #2
Problem 1
A compressed video sequence can be represented by the following autoregressive model equation:
λ(n) = aλ(n− 1) + bω(n), |a| < 1
where ω(n) is a stationary Gaussian white noise (i.i.d.) process with unit variance and average value E(ω) =
η. Show the average bit rate is given by
E(λ) = bη/(1− a), |a| < 1
while the autocovariance function has the exponential decay form of the following equation:
C(n) = σ2λ(a)
n, n ≥ 0
where σ2λ = C(0) = E(λ2)− E2(λ) = b2/(1− a2).
Problem 2
Find the shortest path tree from every node to node 1 in the graph using the Bellman-Ford algorithm.
Problem 3
The number shown next to each link of the network is the probability of the link failing during the lifetime of
a virtual circuit from node A to node B. It is assumed that links fail independently of each other. Find the
most reliable path from A to B, i.e., the path for which the probability that all its links stay intact during
the virtual circuits lifetime is maximal. What is this probability?
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Prof. X. Shen E&CE 710 : Assignment #2
Problem 4
A multiple minisource model is used to model five video sources multiplexed at an access buffer. Each source
generates, on the average, 4.5 Mbits/sec. The standard deviation is σ = 2 Mbits/sec. The autocovariance
time constant is 2.5 sec. The source output is converted to 45-octet cells before transmission to the buffer.
The buffer in turn transmits into the network at a rate of 80,000 cells/sec. Use 20 minisources to model each
video source. Apply fluid analysis to obtain the asymptotic survivor function:
G(x) ∼ Amρme−kx
(Hint: Am = 2.0294× 109)
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