Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
79 views
in Computer by (98.5k points)
closed by
Assuming that packet transmissions and retransmission can both be described as a Poisson process, calculate the probability that a data packet transmission in an S-ALOHA system will experience a collision with another user. Assume the total traffic rate λt = 10 packets/sec and the packet duration τ = 10 msec.
1. 0.9
2. 0.09
3. 0.009
4. 9.0

1 Answer

0 votes
by (95.6k points)
selected by
 
Best answer
Correct Answer - Option 2 : 0.09

The formula to calculate probability in Poisson Process is:

\(P\left( {X = x} \right) = \frac{{{{\left( {\lambda t} \right)}^x}}}{{x!}}{e^{ - \lambda t}}\)

Where:

x = number of success

t = time duration

 = Average number of success during the time duration

Calculation:

Given that, In an S-ALOHA data packet transmission system,

x = experience a collision with another user = 1

t = packet duration

= 10 msec = 10 × 10-3 sec

λ = total traffic rate during packet transmission

= 10 packets/sec

\(\therefore \lambda t = 10 \times 10 \times {10^{ - 3}} = {10^{ - 1}} = 0.1\)

\(\therefore P\left( {X = 1} \right) = \frac{{{{\left( {0.1} \right)}^1}.{e^{ - 0.1}}}}{{1!}}\)

\( = \frac{{0.090}}{1} = 0.090\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...