Aloha Performance
S = New Traffic in Number of frames/unit time
S = 1 ? Fully loaded system
G = New frames + Retransmissions = Total load
P[k frames/unit time] = Gke-G/k!, k=1,2,3,...
P[0] = e-2G , assuming a window of vulnerability of normalized length 2 units = P[no attempts in 2 time units]
P[0] = success rate/attempt rate = S/G.
Equating the above two results, we get: S = Ge-2G
- => Max S = 1/2e, at G=0.5
For Slotted Aloha: S = Ge-G ? Max S = 1/e at G=1