Question

8- Consider an ALOHA system with 10 users, where each user transmits with probability pt = 25%. a) What is the success probability for user #1 [5 pts] b) What is the success probability for any user (u1,u2,....u10) no matter which one: (10 pts] c) In order to increase the success probability would you recommend increasing or decreasing the transmission probability Pt [5 pts] 9-Answer question 8 for a slotted ALOHA system. [20 pts]

Answer 1

solution: Here, it is an ALOHA Sepstern Now, N=10= no. of users P = 25% = probability of foransme 0.25 a) success probability of user 1:- P = Px (1-P)N-1 (1-P)N-1 = 0.25(1-0.25) *** (1-0.25) = 0.25% 0-759x0-759 = 0.250.7518 = 0.25 0.0056377101136 = 0.001408427 = 0.1409 % 6) Success probability for any user in Psuccess = Pit ... + PN = NPq (1-Pt. 2 (N- Psuccess = N PE (1-P) 2(N-1) = 10x0.25 x 0.75' = 0.01409427 18 1.40g427-). the success probability c) In order to increase Prucken I recommend to decrease the transmission probability (P). As can be understood with an enemple - if we torce p = 0.0 greater then 25% suppose) then Psucces = 0.5x0.518 = 1.9773x10 which us much smaller than wher P = 0.25.

decrease it so as to ged the praccess to So, we need to increase . Here, it has slotted Alora system: Criver, N=10 P = 0.25 a) Success probability of usen! :- P, = Pt (1-P)N- = 0.25 X 0.75 = 0.25% 0.075084 -0.01677 -1.877 / b) success probability by any where in Preces a NPq (1-PN- = 10x 0.25 (0.753 = 10x0.01877 - 0.1877 218.772/ or decrease C) Here, I recommend neither sicreate Pt to get success probability As, when P = 0; system nad efficient when Ptali system srcounter collision & hence, not efficient So Neither very small nor very large value of P are efficient so we can to increase the Success probability, maintain the averge value of transmission probability so as to keep it precise