Computer Networks · TEE · formulas

ALOHA formulas and maximum values

All formulas and rules in one place

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

G=\lambda T_fLaTeX: G=\lambda T_f

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

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

Maximum 1/(2e)≈0.18394 at G=0.5.

S_{\mathrm{slotted}}=Ge^{-G}LaTeX: S_{\mathrm{slotted}}=Ge^{-G}

Maximum 1/e≈0.367879 at G=1.

F_{\mathrm{success}}=S/T_fLaTeX: F_{\mathrm{success}}=S/T_f

Convert normalized S into successful frames/s.

B_{\mathrm{success}}=SRLaTeX: B_{\mathrm{success}}=SR

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

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

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

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