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yanalaym [24]
3 years ago
14

(7 3 points) Consider a packet stream whereby packets arrive according to a Poisson process with rate 10 packets/s. If the inter

arrival time between any two successive packets is less than the transmission time of the first, the two packets are said to collide. Find the probability that a packet collides with either its predecessor or its successor assuming that all packets have a transmission time of 20 ms. How will your answer change if the packets have independent, exponentially distributed transmission times
Mathematics
1 answer:
yuradex [85]3 years ago
5 0

Answer:

The answer is below

Step-by-step explanation:

Let t1 be the arrival times between a packet and its immediate predecessor and t2 be the arrival times between a packet and successor. Let L1 be the lengths of the predecessor packet and L2 the length of the packet itself. Therefore:

P(no collision between packet and predecessor or successor) = P(t_1>L_1)P(t_2>L_2)

If P1 is the probability that there is no collision with preceding packets, hence:

P(no collision with other packets) = P_1*P(t_2>L_2)

λ = 10 packets/s, fixed packet length = 20 ms = 0.02 s. Hence:

P(t_1>L_1)=P(t_2>L_2)=e^{-\lambda *0.02}=e^{-10*0.02}=e^{-0.2}

P(no collision between packet and predecessor or successor) = P(t_1>L_1)P(t_2>L_2) = e^{-0.2}*e^{-0.2}=e^{-0.4}

P(packet collides with either its predecessor or its successor) = 1 - P(no collision between packet and predecessor or successor) = 1-e^{-0.4}=0.33

If the transmission times change, the answer would also change.

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alex41 [277]

Answer:

100.26

Step-by-step explanation:

You would find the area of the semi circles on either side of the rectangle by plugging the diameter into the formula for the area of a circle. Then you would add that to the are of the rectangle.

This is what that would look like:

1. Divide 6 (the diameter) by 2 because r=\frac{1}{2} d

r=\frac{1}{2} 6

r=3

2. plug into the formula A=\pi r^{2}

A=\pi 3^{2}

3. square the 3

A=\pi 9

4. multiply 9 by 3.14 (pi)

A=28.26

This means the area of both the semi circles added together would equal 28.26

Then you would use the formula A=lw to find the area of the rectangle

1. plug in the numbers given

A= 12 · 6

2. solve

A=72

Then add the area of the semicircles to the area of the rectangle

A=28.26+72

to get the area of the entire figure:

A=100.26

3 0
3 years ago
Ethan planted a tree that was 1.85 meters tall. Several years later the tree is 5.30 meters tall. Which equation can be used to
PSYCHO15rus [73]

Answer:

5.30 = x + 1.85

x Equals The Difference

7 0
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My name is Ann [436]

Answer:

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Step-by-step explanation:

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You buy 11 bagels with a 20$ bill how m if change do you receive? how many bagels could you buy?
Svetllana [295]
Change you’ll receive is = 0.09
you can only buy 11 because if you divide 20/11 it will give you 1.81 and if you multiply 11x 1.81 it will give you 19.91 which is close to $20 & that’s the most you can buy .
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3 years ago
3[x + 3(4x – 5)] = 15x – 24
Alex17521 [72]

Answer:

\boxed{ \bold{ \huge{ \boxed{  \sf{x = 0.875}}}}}

Step-by-step explanation:

\sf{3[ x + 3(4x - 5)]  = 15x - 24}

Distribute 3 through the parentheses

⇒\sf{3[ x + 12x - 15 ]  = 15x - 24}

Collect like terms : 12x and x

⇒\sf{3[ 13x - 15 ]  = 15x - 24}

Distribute 3 through the parentheses

⇒\sf{39x - 45 = 15x - 24}

Move 15x to left hand side and change it's sign

Similarly, move 45 to right hand side and change it's sign

⇒\sf{39x - 15x =  - 24 + 45}

Collect like terms

⇒\sf{24x =  - 24 + 45}

Calculate

⇒\sf{24x = 21}

Divide both sides of the equation by 24

⇒\sf{ \frac{24x}{24}  =  \frac{21}{24}}

Calculate

⇒\sf{x = 0.875}

Hope I helped!

Best regards! :D

5 0
3 years ago
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