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Consider CSMA/CD protocol, after 4th collision, what is the probability that node choose k=4.
Correct answer is '0.0625'. Can you explain this answer?
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Consider CSMA/CD protocol, after 4thcollision, what is the probability...
First collision, i = min(10, 1)
K={0,……,21-1} = {0,1}
Second Collision, i = min(10, 2)
K= {0,…..,22-1} ={ 0,1 ,2 ,3}
Third Collision i= min(10, 3)
K= {0, ……, 23-1} = {0, 1,2 ,3 ,4 ,5 ,6 ,7}
Fourth collision i=min(10, 4)
K= {0,…….., 24-1} ={0, 1, ….., 15}
Probability to choose k=4 after fourth collision 1/16 = .0625
K={0,……,21-1} = {0,1}
Second Collision, i = min(10, 2)
K= {0,…..,22-1} ={ 0,1 ,2 ,3}
Third Collision i= min(10, 3)
K= {0, ……, 23-1} = {0, 1,2 ,3 ,4 ,5 ,6 ,7}
Fourth collision i=min(10, 4)
K= {0,…….., 24-1} ={0, 1, ….., 15}
Probability to choose k=4 after fourth collision 1/16 = .0625
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Consider CSMA/CD protocol, after 4thcollision, what is the probability...
Understanding CSMA/CD Protocol
The CSMA/CD (Carrier Sense Multiple Access with Collision Detection) protocol is widely used in networking to manage how nodes access a shared communication medium. When collisions occur, nodes must wait and then retry sending data after a random backoff period.
Collision and Backoff Mechanism
- After each collision, a node waits for a random period before attempting to resend.
- The backoff time is determined using a binary exponential backoff algorithm.
- After the nth collision, the node can choose a backoff time randomly from the range [0, 2^n - 1].
Calculating the Probability of k=4 After 4 Collisions
- When a node experiences its 4th collision, it can choose a backoff time from 0 to 15 (2^4 - 1).
- The total possible choices are 16 (0 to 15).
- The choice of k=4 is just one of these 16 possibilities.
Probability Calculation
- The probability P of choosing k=4 after the 4th collision is given by the formula:
P(k=4) = Number of favorable outcomes / Total outcomes
- Here, there is 1 favorable outcome (k=4) and 16 total outcomes:
P(k=4) = 1 / 16 = 0.0625
Conclusion
Thus, the probability of a node choosing k=4 after the 4th collision in the CSMA/CD protocol is indeed 0.0625. This illustrates the randomization process in the backoff mechanism that helps to reduce the likelihood of repeated collisions in network communications.
The CSMA/CD (Carrier Sense Multiple Access with Collision Detection) protocol is widely used in networking to manage how nodes access a shared communication medium. When collisions occur, nodes must wait and then retry sending data after a random backoff period.
Collision and Backoff Mechanism
- After each collision, a node waits for a random period before attempting to resend.
- The backoff time is determined using a binary exponential backoff algorithm.
- After the nth collision, the node can choose a backoff time randomly from the range [0, 2^n - 1].
Calculating the Probability of k=4 After 4 Collisions
- When a node experiences its 4th collision, it can choose a backoff time from 0 to 15 (2^4 - 1).
- The total possible choices are 16 (0 to 15).
- The choice of k=4 is just one of these 16 possibilities.
Probability Calculation
- The probability P of choosing k=4 after the 4th collision is given by the formula:
P(k=4) = Number of favorable outcomes / Total outcomes
- Here, there is 1 favorable outcome (k=4) and 16 total outcomes:
P(k=4) = 1 / 16 = 0.0625
Conclusion
Thus, the probability of a node choosing k=4 after the 4th collision in the CSMA/CD protocol is indeed 0.0625. This illustrates the randomization process in the backoff mechanism that helps to reduce the likelihood of repeated collisions in network communications.
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Consider CSMA/CD protocol, after 4thcollision, what is the probability that node choose k=4.Correct answer is '0.0625'. Can you explain this answer?
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