Table 1 List of some notations used in this paper

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 e_ij

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 ρ_k

\( {P}_{ij}^t \)

Transmission power of link e_ijscheduled in time slot t

\( {f}_{ijt}^{uv} \)

The amount of traffic belongs to traffic session (u, v) ∈ Q passed on link e_ij in time slot t

\( {Z}_{ijt}^{uv} \)

A binary parameter which is equal to 1 if \( {f}_{ijt}^{uv}\succ 0 \)

υ(ρ_k)

The amount of transmitted traffic in one time slot at rate ρ_k

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