System model 上浒充通大学 The network model SHANGHAI JIAO TONG UNIVERSITY >Static networks >Total number of nodes:n >Multicast >Protocol model >Transmission range:r(n)= logn 16
System model The network model 16 ➢Static networks ➢Total number of nodes : n ➢Multicast ➢Protocol model ➢Transmission range: log ( ) n r n n = 1 log n n
System model 上浒充通大￥ Capacity definition SHANGHAI JIAO TONG UNIVERSITY Per-node Throughput:For a given scheme,we define the per-node throughput as the maximum achievable transmission rate.In t time slots,we assume that there are M(i,t) packets transmitted from node i to its destination(s).Firstly,the long term per-node throughput is defined as (n)=lim inf M(i,t) t->00 t Afterwards,the per-node throughput of this model for a given scheme is defined by the maximum T(n)satisfying lim Pr((n)T(n)for all i)=1 n->00 Per-node Capacity:For a given network,the per-node capacity of it is defined as C(n)=max T (n) where o is a scheme for the network,is the set of all possible schemes,and T(n)is the per-node throughput of scheme o. 17
System model Capacity definition 17 Per-node Throughput: For a given scheme, we define the per-node throughput as the maximum achievable transmission rate. In t time slots, we assume that there are M(i,t) packets transmitted from node i to its destination(s). Firstly, the long term per-node throughput is defined as Afterwards, the per-node throughput of this model for a given scheme is defined by the maximum T(n) satisfying t M i t n t i ( , ) ( ) lim inf → = lim Pr( ( ) ( ) for all ) =1 → n T n i i n Per-node Capacity: For a given network, the per-node capacity of it is defined as where is a scheme for the network, is the set of all possible schemes, and is the per-node throughput of scheme . T (n) C(n) max T (n) =