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Range of PDU size
15 years 8 months ago #29843
by longgone
Range of PDU size was created by longgone
A LAN has a data rate of 4Mbps and a propagation delay between two stations at opposite ends of 20 micro secs. For what range of PDU sizes does stop-and-wait give an efficency of at least 50%?
15 years 8 months ago #29849
by TheBishop
Replied by TheBishop on topic Re: Range of PDU size
Is this a school question? If it is, tell us what you've done/thought of so far about how to approach it and we'll help you from there
15 years 8 months ago #29868
by longgone
Replied by longgone on topic Re: Range of PDU size
yes, This is a class ?, here is what I have so far,
(L/ / (L/ + 20us = 50%
(L/ / (L/ + 20us = 50%
15 years 8 months ago #29877
by S0lo
Studying CCNP...
Ammar Muqaddas
Forum Moderator
www.firewall.cx
Replied by S0lo on topic Re: Range of PDU size
I had a shot at it, lets hope it's correct.
Assuming that M in 4Mbps means 1000000. However, in computer terminology M could be 1024x1024 = 1048576. The question did not specify which so I'll use 1000000.
So what I understand from stop-and-wait is that the sender would send a data PDU and wait for an ACK message from the receiver. Once the ACK is received it will send the next PDU and wait again, and so on.
Lets define some variables:
t: The total time to transmit the data PDU (without waiting for ACK).
P: The size of the data PDU (That we need to find a range for)
We know that the Theoretical Speed = 4000000 bps = P / t bps
The total time to send a PDU and wait until we can send the next PDU = t + 20us + ACK time + 20us
The first 20us is obviously the propagation delay for sending the data PDU. The ACK time is not mentioned in the question , so the only way is to ignore it and assume it's equal to zero. the second 20us is the propagation delay of the ACK. The equation reduces to:
t + 40us
We know that efficiency = Actual Speed / Theoretical Speed
Actual Speed = P / (t + 40us) = 4000000t / (t + 40/1000000)
Theoretical Speed = 4000000
Dividing the two to get the efficiency = t / (t + 40/1000000)
The question wants the efficiency to be >= 50%. So
t / (t + 40/1000000) >= 0.5
Resolving the inequality math you will get:
t >= 40 us
But we don't want t. We want P right?. form above we know that P = 4000000 * t. So multiplying both sides of the inequality by 4000000
4000000 * t >= 40 * 4000000 us
P >= 160 bits
So the size of the PDU should be at least 160 bits to achieve an efficiency of 50% or more.
p.s. No guarantees. Please recheck
Assuming that M in 4Mbps means 1000000. However, in computer terminology M could be 1024x1024 = 1048576. The question did not specify which so I'll use 1000000.
So what I understand from stop-and-wait is that the sender would send a data PDU and wait for an ACK message from the receiver. Once the ACK is received it will send the next PDU and wait again, and so on.
Lets define some variables:
t: The total time to transmit the data PDU (without waiting for ACK).
P: The size of the data PDU (That we need to find a range for)
We know that the Theoretical Speed = 4000000 bps = P / t bps
The total time to send a PDU and wait until we can send the next PDU = t + 20us + ACK time + 20us
The first 20us is obviously the propagation delay for sending the data PDU. The ACK time is not mentioned in the question , so the only way is to ignore it and assume it's equal to zero. the second 20us is the propagation delay of the ACK. The equation reduces to:
t + 40us
We know that efficiency = Actual Speed / Theoretical Speed
Actual Speed = P / (t + 40us) = 4000000t / (t + 40/1000000)
Theoretical Speed = 4000000
Dividing the two to get the efficiency = t / (t + 40/1000000)
The question wants the efficiency to be >= 50%. So
t / (t + 40/1000000) >= 0.5
Resolving the inequality math you will get:
t >= 40 us
But we don't want t. We want P right?. form above we know that P = 4000000 * t. So multiplying both sides of the inequality by 4000000
4000000 * t >= 40 * 4000000 us
P >= 160 bits
So the size of the PDU should be at least 160 bits to achieve an efficiency of 50% or more.
p.s. No guarantees. Please recheck
Studying CCNP...
Ammar Muqaddas
Forum Moderator
www.firewall.cx
15 years 8 months ago #29896
by S0lo
Studying CCNP...
Ammar Muqaddas
Forum Moderator
www.firewall.cx
Replied by S0lo on topic Re: Range of PDU size
Your always welcome longgone.
Studying CCNP...
Ammar Muqaddas
Forum Moderator
www.firewall.cx
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