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Final Exam
May 3, 1999
You may use one page of notes and a calculator.
- (15 points) Give expressions for the steady state probabilities of a a Random Arrival, Random Departure (RARD) queue with a queue length of 20, cell arrival probability :2 and cell departure probability :5.
Give an expression for the virtual cell discard probability for a queue carrying traffic from 30 bursty sources, each with a peak data rate of 8% of the link rate and an average data rate equal to 0.5% of the link rate.
The IBA model and virtual cell discard probability can be used to estimate the cell loss for bursty sources. Which is more accurate in each of the following cases? Explain why.
50 bursty sources with peak rate equal to 5% of the link rate, an average rate equal to .5% of the link rate all sending data to a queue large enough to hold one average size burst.
10 bursty sources with peak rate equal to 50% of the link rate, an average rate equal to 5% of the link rate all sending data to a queue large enough to hold 30 average size bursts.
- (10 points) Consider the IP routing table shown below.
prefix next hop
- 3 10* 5 010* 8 1011* 11 00101* 13 100101 9 101100* 12 010110* 7 0100110* 4 1011011* 10 10101111* 7 01001101* 6
What would be the next hop for a packet whose address started with the bits 1011001?
Show a binary trie that could be used to represent this routing table.
- (15 points) Consider a 100 port switching system built using a crossbar with 100 inputs and 200 outputs, with each OPP connecting to two outputs of the crossbar. Suppose all the inputs have a FIFO queue, all the queues are non-empty and that each cell is equally likely to be addressed to any output (and the the addresses are independent of one another). What is the expected number of outputs that get no cells in a single cycle?
What is the expected number that get 1?
What is the expected number that get 2?
How would you modify the time-slotted arbitration ring controller so that it could be used to manage access to this crossbar?
- (15 points) Consider an ATM switch using a Benes network B 512 ; 8 with static routing, together with binary cell replication and recycling for multicast. If all ports are used for both external traffic and for recycling, what speed advantage is needed to ensure that there is no blocking. Assume that 20% of the outgoing traffic is multicast and that the external links operate at 2.4 Gb/s and the maximum virtual circuit rate is 150 Mb/s.
Suppose that the maximum speed advantage that can be implemented in the technology you are using is 4. If you implement multicast by dedicating some of the 512 ports for recycling, how many external ports can the system have?
- (5 points) The table below shows the values of a;b (x) for all values of x from 0 to ab 1. What are the values for a and b?
x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a;b (x) 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15
- (10 points) The figure shown below shows a copy network and related components that can be used in conjunction with a sorting network. The input cells at left are shown with the fanout and multicast index fields (MI). The letters are just labels for identifying the different cells. Show the cells that make it to the fifos just before the final sort & route section, after two operational steps. Write the letters for the cells in the appropriate positions in the fifos.
0, IDQRXW
DGGHU FRQF DGGHU
FRS\ UDQJH
FRS\
URXWLQJ WDEOHV
VRUW
URXWH
D E G H I K
J
F
N
T
Z
U
S
Assume the system operates as described in class. That is, the fanout sums are computed top to bottom and the copy-range block computes the copy network outputs directly, without any regard for positional unfairness.
- (10 points) The following diagram shows a sorting network with 16 inputs and outputs. Draw boxes around the different merge networks that make up the sorting network and label them M 16 , M 8 , M 4 , M 2. For each of the M 4 networks put an arrow to indicate the direction in which its sorting elements sort the values (the arrow should point from largest values to smallest values). Assume that the overall sorting network delivers the smallest values to the top outputs and the largest values to the bottom outputs.
