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Table 1 List of some notations used in this paper

From: Cross layer resource allocation for fault-tolerant topology control in wireless mesh networks based on genetic algorithm

Notation Description
In i Number of radio interfaces of node i
R Set of M available transmission rates
P max Maximum transmission power
Ω Set of non-overlapping channels
ch i Set of channels assigned to node i
G Directed network graph
V Set of n mesh routers
E Set of directed links
e ij Directed link from node i to node j
G ij Propagation gain
d ij Geometric distance between two nodes i and j
SINR ij Signal to Interference and Noise Ratio in the receiver of link eij
γ(ρ) SINR threshold corresponding to the rate ρ
N 0 Thermal noise power
\( {P}_{\mathrm{i}}^{min} \) Minimum transmission power of node i to satisfy K-degree requirement
T max Maximum number of time slots in a time frame
P ij Transmission power from node i to node j
deg i Degree of node i
TD uv The amount of traffic demand from source node u to destination node v
\( {X}_{ijk}^{\omega t} \) A binary variable which is equal to 1 if the transmission from node i to node j is scheduled in time slot t with frequency channel ω and transmission rate ρk
\( {P}_{ij}^t \) Transmission power of link eijscheduled in time slot t
\( {f}_{ijt}^{uv} \) The amount of traffic belongs to traffic session (u, v) Q passed on link eij in time slot t
\( {Z}_{ijt}^{uv} \) A binary parameter which is equal to 1 if \( {f}_{ijt}^{uv}\succ 0 \)
υ(ρk) The amount of transmitted traffic in one time slot at rate ρk
C uv End-to-end average throughput of traffic session (u, v) Q in each time slot
SF uv Satisfaction factor for each traffic session (u, v) Q
\( {\sigma}_{SF}^2 \) Variance of satisfaction factor
\( \overset{\_}{SF} \) Average satisfaction factor of all sessions
\( {\sigma}_{SF}^{2,\max } \) Maximum variance of satisfaction factor
\( {U}_n^i \) Utilization of node i
\( {\sigma}_n^2 \) Variance of \( {U}_n^i \)
\( {\overline{U}}_n \) Average utilization of all nodes
\( {\sigma}_n^{2,\max } \) Maximum variance of node utilization
\( {U}_c^{\omega } \) Utilization of channel ω
\( {\sigma}_c^2 \) Variance of \( {U}_c^{\omega } \)
\( {\overline{U}}_c \) Average utilization of all channels
\( {\sigma}_c^{2,\max } \) Maximum variance of channel utilization