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A
B
C
3c
37 a
2f
22
0 2 1
0
1
2
0
1 2
Ethernet Address
5a
Switch Port Number
Routing Table
Ethernet Address Field
Next Hop Field
D 1
0
2
A
B
C
3c3c
3737 a1a
2f2f
2222
0 2 1
0
1
2
0
1 2
Ethernet Address
5a5a
Switch Port Number
Routing Table
Ethernet Address Field
Next Hop Field
D 1
0
2
Please write clearly. Make your answers concise, but complete.
- (5 points) The figure below shows a small Ethernet network. Assume that initially, none of the routing tables has any valid entries. Show the contents of the routing table following the transmission of a packet by the host with address 5a to the host with address 3c. followed by the transmission of a packet by the host with address 37 to host 5a and a third packet from the host with address 2f to the host with address 37.
CS 577 – Design and Analysis of Switching Systems Exam 1 Jonathan Turner 10 /3/
1 1 0 2 3 3 2 2
4 4 - - 6 7 2 2
4 4 4 4 - - - - 1 1 - - 3 3 3 3
9 9 9 9 - - - - 6 6 6 6 5 5 - - - - - - 7 7 7 7
0 1 2 3 4 5 6 7 1 1 0 2 3 3 2 2
4 4 - - 6 7 2 2
4 4 4 4 - - - - 1 1 - - 3 3 3 3
9 9 9 9 - - - - 6 6 6 6 5 5 - - - - - - 7 7 7 7
0 1 2 3 4 5 6 7
- (10 points) The figure shown below shows an IP address lookup data structure based on a mulitbit trie with a stride of 3 (as described in the paper by Srinivasan and Varghese). Draw a picture of an equivalent binary trie data structure.
- (10 points) Show that the mean of a Pareto distribution with parameters t 0 and α is α t 0 /(α−1).
Show that for 1<α<2, the variance is infinite.
- (10 points) Consider a variation of the RARD queue, in which the arriving packets consist of high priority packets and low priority packets. An arriving high priority packet is added to the queue, if there room in the queue, but a low priority packet is added only if the number of packets currently in the queue is less than or equal to a threshold value. Draw a finite state model for such a queue, assuming the queue has space for a total of four packets and that the threshold is two. Label all the edges with the appropriate transition probabilities. Let the total arrival probability be λ=λ 0 +λ 1 , where λ 0 is the arrival probability for the high priority packets and λ 1 is the arrival probability for the low priority packets (at most one packet arrives during each time step) and let the departure probability be μ.
Write down any two of the steady-state balance equations for your finite state model.
- (15 points) The equation for the virtual loss probability for a queue carrying bursty traffic with exponentially distributed inter-arrival times and burst lengths, an input load of ρ and a burst transmission rate of λ is shown below.
−
/ ( 1 )
(( 1 ) 1 ) !
( / ) λ
ρ λ λ
ρ λ λ i
i i
i i
e
The concept of virtual loss probability can be extended to situations in which traffic of two types is sent over the link. Let ρ j be the input load for traffic of type j , let λ j be the burst transmission rate for traffic of type j. Give an expression for the virtual loss probability for a type 1 source. If ρ 1 =.1, ρ 2 =.5, λ 1 =.5, λ 2 =.1, which type of traffic will experience the higher virtual loss probability? No calculations are necessary, but explain your answer.
B3 A
F
D
C
G
E
label+length weights B3 A
F
D
C
G
E
label+length weights
- (10 points) The queue below shows several packets waiting in queues. At what time does each packet complete transmission on the link, if a GPS scheduler is used? At what time do they finish if a weighted-fair queueing scheduler is used?
