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![EE 333, Communication Networks
Final Exam (2014-15S)
Maximum Marks = 50 Time = 3 hours
1. In the system shown, S transmits on a wireless link.
Therefore, a packet transmitted by S may be received
by both A and B simultaneously. The links A-D and B-
D are wired links. The probability of successful packet
reception for each link is as shown. Assume β1> β2 and
α1= α2= α and that these values are known to A.
Assume that ACKs are error free and the overhead
associated with ACKs can be neglected.
Our measure of system performance N* is the mean of the total number of times a packet has to be
transmitted overall (i.e. by S and by A and/or B) for it to successfully reach D. The following transmission
strategy is used - “S retransmits the packet if it is not received by either A or B. If only one (out of A and
B) receives it then that node is required to forward it to D. If the packet is received by both A and B, then
S selects one of them randomly (equally likely choice) to forward the packet to D.”
(a) Find N* when the above transmission strategy is used. [3]
(b) Consider a modified system, where if both (A and B) receive the packet, then S chooses the one which
would be a better forwarder and asks it to forward the packet to D. Find N* for this. [3]
(c) Consider another modified version of the original system where if both (A and B) receive the packet,
they both transmit to D until the packet is correctly received by the destination. Find N* for this system.
(Hint: Think back to Problem 1 of Quiz-1 to derive the additional result of how many times A and B will
transmit if both have the packet and both transmit.) [4]
2. Consider a single server queue with an infinite buffer where the service times are exponentially
distributed with mean 1/µ. Arrivals to this queue come in batches where each batch always has two
customers and the batches themselves come from a Poisson process with rate λ. Define the system
state as the number in the system. Use ρ=λ/µ for notational purposes.
(a) Draw the state transition diagram [2]
(b) Write the balance equations. [2]
(It would be useful to rewrite them once more in terms of ρ, for later use.)
(c) Find p0 directly from the set of balance equations (infinite set) and the normalization condition.
(Hint: You do not need to find the individual state probabilities explicitly for doing this.) [3]
(d) Use the balance equations to find the generating function P(z) of the system state defined as
0
( ) k
k
k
P z p z
. Confirm the result of (c) by using 1
( ) 1z
P z
[4]
[Hint: Do this by multiplying the kth
equation by zk
, summing both sides for k=1,…,∞ and using
0
1
( ) k
k
k
P z p p z
]
(e) Find the Mean Number in the System, N, using P(z) [2]
(f) What is the Mean Time Spent in System, W, by a customer? [2]](https://image.slidesharecdn.com/end-sem-150427230955-conversion-gate01/85/End-sem-1-320.jpg)
![EE 333, Communication Networks
Final Exam (2014-15S)
Maximum Marks = 50 Time = 3 hours
1. In the system shown, S transmits on a wireless link.
Therefore, a packet transmitted by S may be received
by both A and B simultaneously. The links A-D and B-
D are wired links. The probability of successful packet
reception for each link is as shown. Assume β1> β2 and
α1= α2= α and that these values are known to A.
Assume that ACKs are error free and the overhead
associated with ACKs can be neglected.
Our measure of system performance N* is the mean of the total number of times a packet has to be
transmitted overall (i.e. by S and by A and/or B) for it to successfully reach D. The following transmission
strategy is used - “S retransmits the packet if it is not received by either A or B. If only one (out of A and
B) receives it then that node is required to forward it to D. If the packet is received by both A and B, then
S selects one of them randomly (equally likely choice) to forward the packet to D.”
(a) Find N* when the above transmission strategy is used. [3]
(b) Consider a modified system, where if both (A and B) receive the packet, then S chooses the one which
would be a better forwarder and asks it to forward the packet to D. Find N* for this. [3]
(c) Consider another modified version of the original system where if both (A and B) receive the packet,
they both transmit to D until the packet is correctly received by the destination. Find N* for this system.
(Hint: Think back to Problem 1 of Quiz-1 to derive the additional result of how many times A and B will
transmit if both have the packet and both transmit.) [4]
2. Consider a single server queue with an infinite buffer where the service times are exponentially
distributed with mean 1/µ. Arrivals to this queue come in batches where each batch always has two
customers and the batches themselves come from a Poisson process with rate λ. Define the system
state as the number in the system. Use ρ=λ/µ for notational purposes.
(a) Draw the state transition diagram [2]
(b) Write the balance equations. [2]
(It would be useful to rewrite them once more in terms of ρ, for later use.)
(c) Find p0 directly from the set of balance equations (infinite set) and the normalization condition.
(Hint: You do not need to find the individual state probabilities explicitly for doing this.) [3]
(d) Use the balance equations to find the generating function P(z) of the system state defined as
0
( ) k
k
k
P z p z
. Confirm the result of (c) by using 1
( ) 1z
P z
[4]
[Hint: Do this by multiplying the kth
equation by zk
, summing both sides for k=1,…,∞ and using
0
1
( ) k
k
k
P z p p z
]
(e) Find the Mean Number in the System, N, using P(z) [2]
(f) What is the Mean Time Spent in System, W, by a customer? [2]](https://image.slidesharecdn.com/end-sem-150427230955-conversion-gate01/75/End-sem-1-2048.jpg)
![3. (a) Apply Dijkstra’s Algorithm to the network
shown to find the least cost paths from Node A to all
the other nodes of the network. Show all the steps of
the procedure in detail (cost and path at each step)
and draw the corresponding tree from Node A to the
other nodes of the network. Give the forwarding
table that Node A will finally use to send packets to
the other nodes. [4+2+2]
(b) If Node A wants to multicast to all the other
nodes, what would be the cost of doing this using the
router set up of (a)? [1]
(c) After finding the shortest path from the source (say Node X) to a selected destination (say Node Y),
you want to provide a back-up path which can be used if the any of the links in the shortest path fail.
How would you obtain the best back-up path for achieving this? [1]
4. Give brief answers to each of the following. [1.5x10]
(Remember it is the “quality” rather than the “quantity” which counts. Avoid long-winded answers as
marks will only be given for writing just the key points. 1.5 marks will be given for writing the correct
answer. No part marks will be given!)
(a) Why is Fragmentation and Reassembly incorporated in IPv4?
(b) In IPv4, even though intermediate routers can do fragmentation, reassembly is only done at the
destination. Why?
(c) Why is a NAT useful in configuring an organization’s network?
(d) A NAT violates the principle that the network layers should be kept separate from each other. Why?
(e) What is the “Silly Window Syndrome”?
(f) What is “Slow Start” in TCP?
(g) Why does TCP’s Three-Way Handshake for connection setup make the destination node vulnerable
to a Denial of Service (DOS) attack?
(h) Graceful termination of a TCP connection requires both sides to terminate separately. Why?
(i) What problem does the Nagle Algorithm try to tackle?
(j) TCP’s congestion control mechanism makes a distinction between a “time out” event and the event
of receiving three duplicate ACKs. Why?](https://image.slidesharecdn.com/end-sem-150427230955-conversion-gate01/85/End-sem-2-320.jpg)
End sem
- 1. EE 333, CommunicationNetworks Final Exam (2014-15S) Maximum Marks = 50 Time = 3 hours 1. In the system shown, S transmits on a wireless link. Therefore, a packet transmitted by S may be received by both A and B simultaneously. The links A-D and B- D are wired links. The probability of successful packet reception for each link is as shown. Assume β1> β2 and α1= α2= α and that these values are known to A. Assume that ACKs are error free and the overhead associated with ACKs can be neglected. Our measure of system performance N* is the mean of the total number of times a packet has to be transmitted overall (i.e. by S and by A and/or B) for it to successfully reach D. The following transmission strategy is used - “S retransmits the packet if it is not received by either A or B. If only one (out of A and B) receives it then that node is required to forward it to D. If the packet is received by both A and B, then S selects one of them randomly (equally likely choice) to forward the packet to D.” (a) Find N* when the above transmission strategy is used. [3] (b) Consider a modified system, where if both (A and B) receive the packet, then S chooses the one which would be a better forwarder and asks it to forward the packet to D. Find N* for this. [3] (c) Consider another modified version of the original system where if both (A and B) receive the packet, they both transmit to D until the packet is correctly received by the destination. Find N* for this system. (Hint: Think back to Problem 1 of Quiz-1 to derive the additional result of how many times A and B will transmit if both have the packet and both transmit.) [4] 2. Consider a single server queue with an infinite buffer where the service times are exponentially distributed with mean 1/µ. Arrivals to this queue come in batches where each batch always has two customers and the batches themselves come from a Poisson process with rate λ. Define the system state as the number in the system. Use ρ=λ/µ for notational purposes. (a) Draw the state transition diagram [2] (b) Write the balance equations. [2] (It would be useful to rewrite them once more in terms of ρ, for later use.) (c) Find p0 directly from the set of balance equations (infinite set) and the normalization condition. (Hint: You do not need to find the individual state probabilities explicitly for doing this.) [3] (d) Use the balance equations to find the generating function P(z) of the system state defined as 0 ( ) k k k P z p z . Confirm the result of (c) by using 1 ( ) 1z P z [4] [Hint: Do this by multiplying the kth equation by zk , summing both sides for k=1,…,∞ and using 0 1 ( ) k k k P z p p z ] (e) Find the Mean Number in the System, N, using P(z) [2] (f) What is the Mean Time Spent in System, W, by a customer? [2]
- 2. 3. (a) ApplyDijkstra’s Algorithm to the network shown to find the least cost paths from Node A to all the other nodes of the network. Show all the steps of the procedure in detail (cost and path at each step) and draw the corresponding tree from Node A to the other nodes of the network. Give the forwarding table that Node A will finally use to send packets to the other nodes. [4+2+2] (b) If Node A wants to multicast to all the other nodes, what would be the cost of doing this using the router set up of (a)? [1] (c) After finding the shortest path from the source (say Node X) to a selected destination (say Node Y), you want to provide a back-up path which can be used if the any of the links in the shortest path fail. How would you obtain the best back-up path for achieving this? [1] 4. Give brief answers to each of the following. [1.5x10] (Remember it is the “quality” rather than the “quantity” which counts. Avoid long-winded answers as marks will only be given for writing just the key points. 1.5 marks will be given for writing the correct answer. No part marks will be given!) (a) Why is Fragmentation and Reassembly incorporated in IPv4? (b) In IPv4, even though intermediate routers can do fragmentation, reassembly is only done at the destination. Why? (c) Why is a NAT useful in configuring an organization’s network? (d) A NAT violates the principle that the network layers should be kept separate from each other. Why? (e) What is the “Silly Window Syndrome”? (f) What is “Slow Start” in TCP? (g) Why does TCP’s Three-Way Handshake for connection setup make the destination node vulnerable to a Denial of Service (DOS) attack? (h) Graceful termination of a TCP connection requires both sides to terminate separately. Why? (i) What problem does the Nagle Algorithm try to tackle? (j) TCP’s congestion control mechanism makes a distinction between a “time out” event and the event of receiving three duplicate ACKs. Why?