# ALOHA formulas and maximum values

Subject: Computer Networks

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/cn/#tee/formulas/formulas/aloha

Canonical: https://deep-learning-study-room.vercel.app/read/cn/tee/formulas/formulas--aloha/

Core units, ALOHA, address and routing rules; illustrative values are practice



$$
G=\lambda T_f
$$



λ=aggregate attempts/s; G=attempts/frame time.



$$
S_{\mathrm{pure}}=Ge^{-2G}
$$



Maximum 1/(2e)≈0.18394 at G=0.5.



$$
S_{\mathrm{slotted}}=Ge^{-G}
$$



Maximum 1/e≈0.367879 at G=1.



$$
F_{\mathrm{success}}=S/T_f
$$



Convert normalized S into successful frames/s.



$$
B_{\mathrm{success}}=SR
$$



Successful full-frame bits/s; not necessarily application payload goodput.



$$
P(\mathrm{success\ per\ attempt})=S/G
$$



For G>0. Do not confuse this probability with normalized throughput S.

## Learn it with complete solutions

[Five fully worked rate questions](https://deep-learning-study-room.vercel.app/read/cn/tee/read/aloha--rate-1/)