Performance Analysis(2) k Assumptions Fixed frame length frame time is t New frames generated and retransmitted according to poisson distribution Parameters Throughput S: mean successful frames per frame time osss1 Network load G: mean frames per frame time g>s Successful transmission probability: P0=S/G 2021/2/9 16
Performance Analysis(2) Assumptions Fixed frame length, frame time is t New frames generated and retransmitted according to Poisson distribution Parameters Throughput S: mean successful frames per frame time 0 S 1 Network load G: mean frames per frame time G ≥ S Successful transmission probability: P0=S/G 2021/2/9 16
Performance Analysis(3) P0=P Ino other traffic being initiated during the entire vulnerable period I =e-x2t e -2G (P=(The-A/K!) Throughput: S=G P0=Ge -2G Maximum throughput occurs when G=0.5 S=1/2e≈0.184 2021/2/9
Performance Analysis(3) 2021/2/9 17 P0= P [no other traffic being initiated during the entire vulnerable period ] = e –λ2t = e –2G (P=(λT) K e -λT/K!) Throughput: S = G P0 = G e -2G Maximum throughput occurs when G=0.5, S=1/2e ≈ 0.184
Slotted Aloha Principle divide time into discrete intervals Each interval corresponding to one frame each user must know slot boundaries (synchronization) A2 A1 A2 station A Te new frame B1 station B final effect 2021/2/9
Slotted Aloha Principle: divide time into discrete intervals Each interval corresponding to one frame Each user must know slot boundaries (synchronization) 2021/2/9 18 A1 new frame B3 A2 A2 B1 collision t1 t2 B2 B2 B3 A3 station B final effect A1 B1 B2 A2 A3 station A
Performance Analysis(1) Po=Pi arrival interval>t] =e=e-G Throughput s=G×P0=Ge g Maximum throughput occurs when G=1, S=1/e≈0.368 2021/2/9
Performance Analysis(1) P0= P [ arrival interval> t ] = e - λ t = e –G Throughput S = G P0 = G e –G Maximum throughput occurs when G=1, S=1/e ≈ 0.368 2021/2/9 19 t t
ALOHA Summary 0.40 Slotted ALOHA:S= Ge-G 0.30 0.20 30.10 Pure ALOHA:S= Ge-2G 0.5 1.0 1.5 2.0 3.0 G(attempts per packet time Throughput versus offered traffic for ALOHA systems 2021/2/9 20
ALOHA Summary 2021/2/9 20 Throughput versus offered traffic for ALOHA systems