TSMG 5320 HW4

TSMG 5320 – HW #4 – Spring 2011
Homework assignments are to be worked individually – and without access to solutions of any previously assigned homework. Please review the posted policy on Academic Integrity and Plagiarism. Show all work for full credit.
Problem 1
We need to carry a series of DS-3 frames in STS-1 frames. The SPE pointer in each frame points to the 9th octet in the 3rd row of the payload. Show graphically how the data octets are mapped to the STS-1 frames – it’s sufficient to sketch the first two SONET frames only. For each of these frames, calculate the total overhead transmitted, and the payload as a % of the total transmission (ie, fraction of time spent transmitting actual data).
Problem 2
The maximum user data rate for OC-3 is 148.608 Mbps. Derive this rate from the SONET STS-3 parameters.
Problem 3
The 4-node SONET ring shown below has the following end-to-end (ie, path-level) traffic matrix:
A B C D
A 2 3 5
B 2 4 6
C 1 5 2
D 8 4 3
Assume all traffic loads are in units of STS-1s.
Find the total working and protection traffic flows on each link of the ring in each direction if
(a) a UPSR ring is used,
(b) a BLSR/2 ring is used. (Use a separate diagram for each case.)
Problem 4
Now for each of the rings of Problem 3, assume that both optical links between C and D are severed. In both cases, find the flows on each link in each direction. (Again, use 2 separate diagrams.)
Problem 5
A DWDM system uses optical carriers Δf apart. Show that the corresponding wavelength separation Δλ is given approximately by
Δλ = (λ2/c) Δf
where λ is the reference wavelength of the optical band and c is the speed of light. For the 1.55 μm band and interchannel spacings of 25 GHz, calculate the corresponding spacing of the wavelengths.
Problem 6
Consider an optical system which is emitting light in both the 1300 and 1550 nm optical windows. If the wavelength spacing is about 0.4 nm, what is the maximum number of DWDM carriers possible? (Assume the 1300 and 1550 nm windows run from 1230 to 1390, and 1420 to 1625, respectively.)
Calculate the corresponding spacing of the carriers in Hertz and the total bandwidth potentially available.
If the line coding scheme used provides a spectral efficiency of 0.4 bps/Hz, what is the peak data rate that a single fiber optic strand can support?
Problem 7
Consider the network shown below. (Ignore all λs on the diagram.)
Let the connection requests be as follows:
B-G, A-E, B-D, D-F, B-F, C-E, C-H, A-H, A-C
Set up lightpaths to satisfy the above set of requests assuming only 3 wavelengths are available on each link. Assume no wavelength conversion in the optical core, ie, no λ conversion in nodes 1 thru 10.
Problem 8
For the same network, we wish to establish the following seven lightpaths:
C-7-8-9-E
A-1-5-8-9-E
H-2-1-5-8-7-C
B-6-7-8-9-E
A-1-6-7-10-D
G-3-2-1-6-B
H-2-3-4-F
Color these lightpaths using the minimum number of wavelengths. Again, assume no wavelength conversion.
Problem 9
(a) The availability of a link is required to be 0.999. What is the maximum amount of time that that the link is allowed to be down in a year?
(b) Nodes A and B are connected by two links in tandem. If the availability of each link is 0.99, what is the availability of the A to B connection? Assume links fail independently.
(c) Nodes A and B are connected by two parallel links in tandem, with 1+1 protection used. If the availability of each link is 0.99, what is the availability of the A to B connection? Again assume links fail independently.。