Set of speech packets are queued up for tranmission
A set of speech packets are queued up for transmission in a network. If there are twelve packets in the queue, the total delay D until transmission of the twelfth packet is given by the sum D = T1 + T2 +. . .+T12 where the T1 are IID exponential random variables with mean E{Ti} = 8 ms. What is the variance Var[Ti]? (You may refer to the formulas on the inside cover of the text.) Find the mean and variance of the total delay D. Speech packets will be lost if the total delay D exceeds 120 ms. Because D is the sum of IID exponential random variable is given [10, p. 172] where is the parameter describing the exponential random variables Ti. Using this result, compute the probability that packets are lost, that is, Pr[D > 120]. By applying the Central Limit Theorem and using the Gaussian distribution, compute the approximate value of Pr[D > 120]. Compare this to the exact result computed in part (c).
Solution
a). 0.667
b). mean= 8 & variance= 0.7933
.
Set of speech packets are queued up for tranmission A set of speech pa.docx
1. Set of speech packets are queued up for tranmission
A set of speech packets are queued up for transmission in a network. If there are twelve packets
in the queue, the total delay D until transmission of the twelfth packet is given by the sum D =
T1 + T2 +. . .+T12 where the T1 are IID exponential random variables with mean E{Ti} = 8 ms.
What is the variance Var[Ti]? (You may refer to the formulas on the inside cover of the text.)
Find the mean and variance of the total delay D. Speech packets will be lost if the total delay D
exceeds 120 ms. Because D is the sum of IID exponential random variable is given [10, p. 172]
where is the parameter describing the exponential random variables Ti. Using this result,
compute the probability that packets are lost, that is, Pr[D > 120]. By applying the Central Limit
Theorem and using the Gaussian distribution, compute the approximate value of Pr[D > 120].
Compare this to the exact result computed in part (c).
Solution
a). 0.667
b). mean= 8 & variance= 0.7933
![Set of speech packets are queued up for tranmission
A set of speech packets are queued up for transmission in a network. If there are twelve packets
in the queue, the total delay D until transmission of the twelfth packet is given by the sum D =
T1 + T2 +. . .+T12 where the T1 are IID exponential random variables with mean E{Ti} = 8 ms.
What is the variance Var[Ti]? (You may refer to the formulas on the inside cover of the text.)
Find the mean and variance of the total delay D. Speech packets will be lost if the total delay D
exceeds 120 ms. Because D is the sum of IID exponential random variable is given [10, p. 172]
where is the parameter describing the exponential random variables Ti. Using this result,
compute the probability that packets are lost, that is, Pr[D > 120]. By applying the Central Limit
Theorem and using the Gaussian distribution, compute the approximate value of Pr[D > 120].
Compare this to the exact result computed in part (c).
Solution
a). 0.667
b). mean= 8 & variance= 0.7933](https://image.slidesharecdn.com/setofspeechpacketsarequeuedupfortranmissionasetofspeechpa-230201031605-494d1415/85/Set-of-speech-packets-are-queued-up-for-tranmission-A-set-of-speech-pa-docx-1-320.jpg)
