Throughput of Slotted Aloha The throughput is the fraction of slots that contain a successful transmission P(success)=ge9 When system is stable throughput must also equal the external arrival rate (2) Departure rate ge s=e 8-ge 8=0 What value of g dg(n maximizes throughput? →g= g<1=> too many idle slots g>1=> too many collisions →P( success)=ge=1/e≈0.36 If g can be kept close to 1, an external arrival rate of 1/e packets per slot can be sustainedλ Throughput of Slotted Aloha • The throughput is the fraction of slots that contain a successful transmission = P(success) = ge-g – When system is stable throughput must also equal the external arrival rate (λ) -1 e Departure rate ge-g 1 g d – What value of g dg n ge − g = e− g − ge− g = 0 ( ) maximizes throughput? ⇒= g 1 – g < 1 => too many idle slots – g > 1 => too many collisions ⇒ P(success) = ge− g = 1/ e≈ 0.36 – If g can be kept close to 1, an external arrival rate of 1/e packets per Eytan Modiano Slide 9 slot can be sustained