# Probability in Dynamic frame aloha

If I've RFID Collision Arbitration System that is based on multi-frame dynamic frame ALOHA. How can compute the probability of the average tag resolution $L_n$? ,$P_s$ is probability for packet trasmission that no other packet arrives in the previus slot. $P[N(t+T,t)=0)]=e^G ; S=Ge^G$;S stand for Throughput.

$G=Tx\lambda$ G is traffic Distribuited according to Poisson process end $\lambda$ is Packet arrivals poisson process with paratameter $\lambda$ end T is last trasmission.

Knowing that $N_{population Tag=}=5$ end $r_{slotsize}=3$? i'know that if i want to compute $L_n$, i've to apply recursive formula, that is : $$L_n=r+\sum_{i=0}^n P(S=i)L_{n-i}$$ end in this case i'd have to obtain :

$$L_5= 3+P(S=0)L_5+P(S=1)L_4+P(S=2)L_3P(S=3)L_2P(S=4)L_1P(S=5)L_0$$ for me here it's ok until i've to compute P(S=0)...but for the other how could compute it?

• It's impossible to answer your question until you explain what $S$ stands for and what is its distribution. Of course, once you know the distribution, you should be able to calculate everything on your own. – Yuval Filmus Sep 4 '17 at 20:56
• What do you mean by "average resolution"? What is $I$? Please edit the question to include all information in the question and make it read well for someone who encounters it for the first time. Don't leave clarifications in the comments -- we want people ot be able to understand the question without having to read the comments. Thank you! – D.W. Sep 5 '17 at 5:37
• What's an "averange tag resolution"? I suspect you mean "average tag resolution", but what is that? What does the random variable $G$ represent? What does $\lambda$ represent? I can't understand your explanation of them. What do you mean by "last transmission"? What is $r$? If you're getting this from somewhere, can you cite the source? – D.W. Sep 5 '17 at 21:23
• home.deib.polimi.it/cesana/teaching/IoT/2017/classes/9.RFID.pdf (From page 26 to 33) – Alb084 Sep 6 '17 at 8:08