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The problem formulation are:
R
the set of all mesh routers
N
number of mesh routers
K
the maximum number of antennas that is allowed to be installed in a mesh router
auv
the indicator function which is 1 if a direct wireless link is formed between mesh
routers u and v, and 0 otherwise, auu = 0
λu
the traffic demand of mesh router u
tuv
the traffic load offered by mesh routers u to v. tuv≥0, tuu = 0
cuv
link capacity of the wireless link between mesh routers u and v. cuv≥0, cuu = 0
δuv
the indicator function which is 1 if mesh router u is a gateway and 0 otherwise
σu
the cost on setting up mesh router u as a gateway
D
the maximum tolerable delay
du
the maximum delay of mesh router u
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 σu, 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- δu)ni,j = 0
where ni,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.
(a) Since APPL and MSFT account for the entire large cap technology component of S&P 500 and their proportion of index is based on their weights, this large cap technology sector
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