Given: Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets. To find: Probability (p) that the node “A” succeeds for the first time in slot number 5. Solution: The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A)) 4 p(A) --- (1) . Here, p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit). p(A)=p ( A transmit ) * p ( B does not transmit ) * p ( C does not transmit ) * p(D does not transmit)

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Answer 1

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

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Suppose nodes A, B, C and D are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability p = 0.6. The first slot is numbered slot 1, the second slot is numbered slot 2, and so on. a) What is the probability that node A succeeds for the first time in slot 5? b)What is the probability that some node (either A, B, C or D) succeeds in slot 4? c) What is the probability that the first success occurs in slot 3? d) What is the efficiency of this four-node system?

Suppose four active nodes—nodes A, B, C and D—are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability . The first slot is numbered slot 1, the second slot is numbered slot 2, and so on. (a) What is the probability that node A succeeds for the first time in slot 5? (b) What is the probability that some node (either A, B, C or D) succeeds in slot 4? (c) What is the probability that the first success occurs in slot 3? (d) What is the efficiency of this four-node system?

Suppose nodes A and B are on the same 10 Mbps broadcast channel, and the propagation delay between the two nodes is 245 bit-times. Suppose A and B send Ethernet frames at the same time. Suppose the transmission time of the entire frame is 295 bit-times. So, the frames collide, and then A and B choose different values of K in the CSMA/CD algorithm. A node chooses the value of K at random from {0,1,2,...2n−1} where n is the number of collisions experienced on the channel – note n is set to 1 in this case). For Ethernet, the actual amount of time a node waits is K*512 bit times (i.e., K times the amount of time needed to send 512 bits into the Ethernet). Suppose A chooses a K value of 0 and B chooses a K value of 1. Assuming no other nodes are active, can the retransmissions from A and B collide? Justify your answer by showing all the intermediate steps of your calculations.

Answer 2

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 8

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

Answer 9

Chapter 6, Problem P11P

a.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that the node “A” succeeds for the first time in slot number 5.

Solution:

The probability (p) that the node “A” succeeds for the first time in slot number 5 is (1-p(A))4p(A) --- (1).

Here,

p (A) is the probability that the node “A” succeeds in any slot. That is: p (A transmits, B, C, and D does not transmit).

p(A)=p(A transmit) * p(B does not transmit) * p(C does not transmit) * p(D does not transmit)

Answer 10

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

Answer 11

b.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that any of the nodes “A”, “B”, “C”, or “D” succeeds in slot number 4.

Solution:

From (a), it is clear that if any node succeeds in any slot, the probability is p(node)=p(1-p)3.

So,

The probability that the node “A” succeeds in slot number 4 is: p(A)=p(1-p)3

The probability that the node “B” succeeds in slot number 4

Answer 12

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

Answer 13

c.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Probability (p) that 1^st success occurs on slot number 3.

Solution:

Probability of some node occurs in a slot = 4p(1-p)3

Probability of no node succeeds in a slot = 1-4p(1-p)3

Probability of the first success occurs in slot number 3 is determined by multiplying the probability of some node succeeds in a slot and probability of no node succeeds in a slot.

Let p(S) = probability of the 1^st success occurs in slot number 3

Answer 14

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 15

d.

Explanation of Solution

Given:

Consider that there are four nodes “A”, “B”, “C”, and “D”. These four nodes are active and competing for access to a channel using slotted ALOHA. Each nodes have infinite number of packets.

To find: Efficiency of the four node system.

Solution:

The efficiency of the four node system is determined by the success of any nodes succeeds in a slot...

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 6 - Consider the transportation analogy in Section...Ch. 6 - If all the links in the Internet were to provide...Ch. 6 - Prob. R3RQ Ch. 6 - Prob. R4RQ Ch. 6 - Prob. R5RQ Ch. 6 - Prob. R6RQ Ch. 6 - Prob. R7RQ Ch. 6 - Prob. R8RQ Ch. 6 - Prob. R9RQ Ch. 6 - Prob. R10RQ

Solution Summary: The author explains how to find the probability that the node "A" succeeds in slot number 5 by substituting the value of p (A) in equation (1).

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

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Chapter 6 Solutions