The problem formulation are:

The WMN design problem is then formulated as:

The cost on setting up an antenna and setting mesh router u as a gateway is normalized as 1 and σ_u, respectively. Constraint (C1) represents the degree constraint on mesh routers, while constraint (C2) requires that the offered load of mesh routers u to v does not exceed the link capacity. Constraint (C3) requires traffic balance for each non-gateway mesh router. Besides, for a gateway mesh router, no traffic demand is present and a gateway does not offer traffic load to other mesh routers. Constraint (C4) requires that all traffic demands are served by gateways. Constraint (C5) means that a link is formed by two opposite antennas. Constraint (C6) requires that the maximum packet delay of each mesh router is within an acceptable range.

Moreover, for the sake of survivability, the WMN requires that each non-gateway mesh router should have at least two node-disjoint paths to different gateways. Therefore a WMN must meet the following survivability

requirement:

                              ? i,j ?  (1- δ_u)n_i,j  = 0

where n_i,j denotes the number of common nodes among mesh router u's ith and j th paths.

Use directional antenna and node operate in Time division duplex (TDD) mode with BWMN.

Traffic demand of mesh router is composed of client's effective traffic demands.