GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
204 views
In a aloha implemented shared channel probability of transmission of a station in a time span of T is p. Given, probability such that NO station transmit in a time duration of $2T$ is $50\%$ , where T = one frame transmission time. What is the value of p is if total no of station = $100$
asked in Computer Networks by Veteran (50.9k points)  
edited by | 204 views
is aloha in gate 2017 syllabus ?
Yes both pure and slotted aloha as they are collision detection techniques in MAC sublayer.

"Given, probability such that NO station transmit in a time duration of 2T" implies vulnerable time = 2G, 

 as T = frame transmission time which is for pure aloha , then why question says slotted aloha .??

What I think, In poisson distribution we can consider any time span and calculate some required probability irrespective of how small the probability comes out to be. Whether it is slotted or not in this question , concerned time span of time is 2T. (it can be anything like 3.2T etc. for this question)
okk, so wht is P , prob. of success ?
probability of transmission of a station in a time span of T is p.

1 Answer

+2 votes

I did in the following way,

For any time span probability of there being x transmission attempts is

$$\frac{A^xe^{-A}}{x!}$$

Where A is the average no of transmission attempt in that time span.

In that question time duration is $2T$ . And we know that channel load G is the average transmission attempt in T time duration. So, in 2T time the average transmission attempts will be 2G.

SO, plugging A = 2G in the above formula,

$$\frac{(2G)^xe^{-2G}}{x!}$$

For the given condition , No transmission attempts is 2T  => x = 0

Probability = $\frac{(2G)^0e^{-2G}}{0!}$ = 0.5

=> G = 0.3465

Now for poisson Mean of average is  = Np

=> p = 0.003465 (very low)

answered by Veteran (50.9k points)  
I also did in the same way, and its only what i m getting and even i am not getting any other approach to solve this .
same !


Top Users Aug 2017
  1. Bikram

    4902 Points

  2. ABKUNDAN

    4704 Points

  3. akash.dinkar12

    3480 Points

  4. rahul sharma 5

    3158 Points

  5. manu00x

    3012 Points

  6. makhdoom ghaya

    2480 Points

  7. just_bhavana

    2388 Points

  8. stblue

    2138 Points

  9. Tesla!

    2060 Points

  10. joshi_nitish

    1758 Points


25,014 questions
32,139 answers
74,822 comments
30,185 users