Throughput of Slotted Aloha The throughput is the fraction of slots that contain a successful transmission= P(success)= g(n)e-g(n) When system is stable throughput must also equal the external arrival rate(a) Departure rate g(n)e-g(n) g(n) What value of g(n) gn)e g(m)=e gtn)-g(n)e-tn) maximizes throughput? lg(n) g(m)=1 g(n)<1>too many idle slots g(n)>1=> too many collisions P(success)=(n )e g(m)=1/ex0.36 If g(n)can be kept close to 1, an external arrival rate of 1/e packets per slot can be sustainedThroughput of Slotted Aloha • The throughput is the fraction of slots that contain a successful transmission = P(success) = g(n)e-g(n) – When system is stable throughput must also equal t he external arrival rate ( λ) -1 e Departure rate g(n)e-g(n) 1 g(n) – What value o f g(n) maximizes throughput? – g(n) < 1 => too many idle slots – g(n) > 1 => too many collisions – If g(n) can be kept close to 1, an external arrival rate of 1/e packets per slot can be sustained d dg ( n ) g ( n ) e − g(n) = e − g(n) − g ( n ) e − g(n) = 0 ⇒ g ( n ) = 1 ⇒ P (success ) = g ( n ) e − g(n) = 1/ e ≈ 0.36 Eytan Modiano Slide 10