Nt1330 Unit 6 Case Study

Preprocessing

This preprocessing step is done before the considered two cases of not split table traffic amounts and the split table traffic amounts. It includes the network topology design as follows:
-Select the number of nodes (n) and the terrain area.
-Generate randomly the locations (co-ordinates) of the n nodes using the uniform distribution.
-Find the distance matrix between each node pairs.
-Assume the transmission range of each node (usually all the nodes have the same range).
-Find the neighbors according to the distance between nodes and the transmission range.
-Determine the connectivity matrixX_(i,j), where each matrix element x_(i,j) is a Boolean variable, such that x_(i,j) =1 if there is a link from node i to node j; otherwise, x_(i,j) , = 0.

Problem

P_max , maximally allowed transmitting power of nodes.

Output variables:

y_(i,j)^(s,d) , Boolean variables, y_(i,j)^(s,d) =1 if the route from s to d goes through the link (i, j); otherwise y_(i,j)^(s,d)= 0.

Objective function:

Minimize the total power consumption of nodes. Min ∑_((i,j))▒E_(ij ) × y_( i,j)^(s,d)

Constraints:

Delay constraint: ∑_((i,j))▒y_(i,j)^(s,d) "≤ " H_(s,d) ∀ (s,d) (5)

This constraint ensures that the hop-count for each node-pair (s, d) does not exceed the pre-specified bound〖 H〗_(s,d). Bandwidth constraint:

∑_((s,d))▒∑_j▒y_(i,j)^(s,d) T_(s,d) "+" ∑_((s,d))▒∑_j▒y_(j,i)^(s,d) T_(s,d) "≤ B ∀ " i"∈ V" (6)

The availability of bandwidth along the route is ensured by this constraint.

- Transmitting power constraint: d_(i,j)^∝ x_(i,j) ≤ P_max ∀ i