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Table 1 Summary of notations

From: QoS-aware routing for heterogeneous layered unicast transmissions in wireless mesh networks with cooperative network coding

 

Summary of notations

G(N,E)

Directed graph that represents a wireless mesh network

N

Set of nodes in the network

E

Set of links in the network

(a,b)

Link conveying data from node a to node b

t(l)

Transmitter node of link l

r(l)

Receiver node of link l

T O (n)

Set of outgoing links of node n

T I (n)

Set of incoming links of node n

Γ

Set of all pairs of source and destination nodes in the network

(s,d)

Pair of source node s and destination node d of an arbitrary unicast session

c l

Normalized capacity of link l

p l

Probability of packet loss of link l

M ¯ ( s , d )

Number of the original layers of data transmitted by (s,d)

L i ¯ ( s , d )

i ¯ th

layer of (s,d)

r i ¯ ( s , d )

Transmission rate of i ¯ th layer of (s,d)

I M ¯ ( s , d )

Set of layer indices of (s,d), where I M ¯ ( s , d ) ={0,1,2,, M ¯ ( s , d ) 1}

t ¯

Normalized transmission rate

M (s,d)

Number of sublayers of (s,d), where M ( s , d ) = i ¯ I M ¯ ( s , d ) r i ¯ ( s , d ) / t ¯

M

Maximum number of sublayers that a source send to a destination in a network

L i ( s , d )

The i th sublayer of (s,d)

I M

Set of sublayer indices, where I M ={0,1,2,…,M−1}

P i ( s , d )

Probability of a successful packet transmission for L i of (s,d) called the reliability

f l , i ( s , d )

0 to 1 variable that indicates whether or not link l is used to transmit a packet of L i for (s,d)

R i ( s , d )

Set of links used to transmit packets of sublayer L i from source s to destination d

x i ( s , d )

0 to 1 variable that indicates whether or not packets of sublayer L i are transmitted from source s to destination d

κ i ( s , d )

Information value of L i ( s , d ) used to prioritize data sublayers

q i ( s , d )

QoS requirement of sublayer L i ( s , d )

J

Set of indices for all independent sets

Z j

Set of parameters indicating the links that can be activated at the same time according to the j th independent set

z l j

Variable that indicates whether or not link l can be activated in the j th independent set

a j

Activation time fraction of the j th independent set in each time slot

γ

Tuning parameter of the alternative objective function, where 0<γ<1