One author said in his journal:
If there are some transmitters, each transmitting packet(s) every 20ms.
T_duplicate is the delay caused by collision of packets when two or more transmitters transmit packets at the same time.
E.g. if there are 4 transmitters, the T_duplicate is given by:
T_duplicate=Summation[i=1,inf]20*i*P(i) (1)
where P(i) is the probability that the receiver needs more time to receive i overlapped packet(s) in the time domain.
(1) contains a constant of 20, because the receiver needs 20i more milliseconds if i transmitters broadcast their packets at the same time.
We analyze P(i) in a case by case manner. For example, if n is the number of transmitters =4, P(i) is given by:
P(1)=(2)^n*((1/20)^2)*(19/20^(n-2)) (2)
P(2)=(3^n)*((1/20)^3)*(19/20^(n-3)) (3)
P(3)=(4^n)*((1/20)^4)*(19/20^(n-4)) (4)
where (2) indicates the probability that 2 transmitters broadcast packets at the same time. In this case, the receiver will experience 20ms additional delay to receive a packet in next broadcasting period. On the other hand, (3) implies the probability that 3 transmitters transmit packets at the same time, In this case, the receiver needs additional time of 40ms. Finally, (4) indicates the probability that 4 transmitters broadcast packets at the same time. In this case, there will be 60ms additional delay.
My question is: Has the author made a mistake as equation (1) will not converge?
Do you think equation (1) should be as follows:
T_duplicate=(Summation[i=1,2]20*i^P(1))-20 when 2 transmitters broadcast at the same time.
T_duplicate=(Summation[i=1,3]20*i^P(2))-20 when 3 transmitters broadcast at the same time.
T_duplicate=(Summation[i=1,4]20*i^P(3))-20 when 4 transmitters broadcast at the same time.
In other words,equation (1) should be as follows:
T_duplicate=(Summation[i=1,N]20*i^P(i))-20, where N is the number of transmitters broadcasting packets at the same time.
Or, am i confused?
Please any help would be appreciated. and if any one has any suggestion about equation (1), and how it should be.
Any comments about equations (2),(3)and (4) ?.
Thank you.
If there are some transmitters, each transmitting packet(s) every 20ms.
T_duplicate is the delay caused by collision of packets when two or more transmitters transmit packets at the same time.
E.g. if there are 4 transmitters, the T_duplicate is given by:
T_duplicate=Summation[i=1,inf]20*i*P(i) (1)
where P(i) is the probability that the receiver needs more time to receive i overlapped packet(s) in the time domain.
(1) contains a constant of 20, because the receiver needs 20i more milliseconds if i transmitters broadcast their packets at the same time.
We analyze P(i) in a case by case manner. For example, if n is the number of transmitters =4, P(i) is given by:
P(1)=(2)^n*((1/20)^2)*(19/20^(n-2)) (2)
P(2)=(3^n)*((1/20)^3)*(19/20^(n-3)) (3)
P(3)=(4^n)*((1/20)^4)*(19/20^(n-4)) (4)
where (2) indicates the probability that 2 transmitters broadcast packets at the same time. In this case, the receiver will experience 20ms additional delay to receive a packet in next broadcasting period. On the other hand, (3) implies the probability that 3 transmitters transmit packets at the same time, In this case, the receiver needs additional time of 40ms. Finally, (4) indicates the probability that 4 transmitters broadcast packets at the same time. In this case, there will be 60ms additional delay.
My question is: Has the author made a mistake as equation (1) will not converge?
Do you think equation (1) should be as follows:
T_duplicate=(Summation[i=1,2]20*i^P(1))-20 when 2 transmitters broadcast at the same time.
T_duplicate=(Summation[i=1,3]20*i^P(2))-20 when 3 transmitters broadcast at the same time.
T_duplicate=(Summation[i=1,4]20*i^P(3))-20 when 4 transmitters broadcast at the same time.
In other words,equation (1) should be as follows:
T_duplicate=(Summation[i=1,N]20*i^P(i))-20, where N is the number of transmitters broadcasting packets at the same time.
Or, am i confused?
Please any help would be appreciated. and if any one has any suggestion about equation (1), and how it should be.
Any comments about equations (2),(3)and (4) ?.
Thank you.
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