Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
Expert Solution & Answer
Book Icon
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 1st 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 1st 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...

Blurred answer
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Computer Networking: A Top-Down Approach (7th Edi...
Computer Engineering
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:PEARSON
Text book image
Computer Organization and Design MIPS Edition, Fi...
Computer Engineering
ISBN:9780124077263
Author:David A. Patterson, John L. Hennessy
Publisher:Elsevier Science
Text book image
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:9781337569330
Author:Jill West, Tamara Dean, Jean Andrews
Publisher:Cengage Learning
Text book image
Concepts of Database Management
Computer Engineering
ISBN:9781337093422
Author:Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:Cengage Learning
Text book image
Prelude to Programming
Computer Engineering
ISBN:9780133750423
Author:VENIT, Stewart
Publisher:Pearson Education
Text book image
Sc Business Data Communications and Networking, T...
Computer Engineering
ISBN:9781119368830
Author:FITZGERALD
Publisher:WILEY