Question

A large population of Aloha users manages to generate 50 requests/sec, including both originals and retransmissions. Time is slotted in units of 40 msec.a. What is the chance of success on the first attempt at a given station?b. What is the probability of exactly k collisions (for k = 1, 2,...,10) followed by a success?c. What is the expected number of transmission attempts needed?

Answer 1

Answer:

a) 0.1353

b) attached below

c) 7.4

Explanation:

Frame transmission rate = 40 msec

Total load  requests = 50 requests /sec

hence

Total arrival rate G in Frames ( G ) / x secs

= 50 request/sec * X sec

= 50 * ( 40*10^-3 )

= 2 requests/ x sec

a) Determine chance of success on first attempt

0.1353

b) Determine the probability of exactly K collisions followed by a success

 attached below

c) what is the expected number of transmission attempts needed

7.4