What is the difference between the full_grid and the sparse_grid Wireless Domain Models? When should I use the full_grid and when should I use the sparse_grid?

What is the difference between the full_grid and the sparse_grid Wireless Domain Models? When should I use the full_grid and when should I use the sparse_grid?

Full-grid is the simplest wireless domain model. With the full-grid, you divide a rectangular region in rectangular cells, like tiles. This is where the attributes x cell number and y cell number come into picture. x cell number is the number of cells along the horizontal axis that the rectangular region has been divided into. y cell number is the number of cells along the vertical axis that the rectangular region has been divided into. Thus the entire rectangular region contains x cell number * y cell number cells. Note that the x span refers to the length of the rectangular region, y span to the height of the rectangular region. The full-grid model is used as follows: all the wireless nodes that fall within a cell will form a set. Thus tessellating the rectangular region will split the wireless nodes in the region in disjoint sets. When two nodes, one in the set corresponding to cell A and the other in the set corresponding cell B are communicating, some pipeline stage computations (closure, channel match, propagation delay, path loss) are saved. Later, when another node in the first set, talks with a node in the second set, we use the same pipeline stage computations saved when the first pair communicated. Our assumption is that the stored pipeline computation that was exact for the first pair of communicating nodes will be approximately same for the second pair of communicating nodes, provided the two pairs both belongs to same cartesian product {Set of nodes in cell A}X{Set of nodes in cell B}. Now, how you decide to divide the rectangular region of the wireless domain model (i.e. in how many cells) depends on how coarse you want to make the approximation that substitutes the pipeline stage computation of one pair of nodes with the pipeline stage computation of another pair of nodes. The more cells you make, until each cells contains only one wireless node, the lesser the degree of approximation. Now the sparse-grid model does not bring any new functionality besides what the full-grid can offer you. The sparse-grid is just geared towards reducing the space of memory allocated for saving key pipeline computation. Imagine you have a rectangular area, that is very sparsely populated with wireless nodes. Say your rectangular area has 10 cells on the horizontal, 10 on the vertical, for a total number of 100 cells. Suppose only 2 cells out of the 100 cells contain wireless nodes. In the full-grid mode, we reserve memory for saving computations for all the pairs between 100 cells (i.e. we reserve memory of the order of 100^2 pairs), but we only need memory for 1 pair. In order to prevent this memory inefficiency, we introduce the idea of groups in the sparse grid. This works as follows: we partition the horizontal cells into groups; similarly, we partition the vertical cells. For instance, we can divide the 10 horizontal cells into 5 groups of 2 consecutive cells; we divide the 10 vertical cells into 5 groups of 2 consecutive cells. This is done by setting the x group size to 2, and the y group size to 2. Thus, the 100 cells will be divided in 5*5 = 25 groups across the whole rectangle. We only allocate memory on a per-group basis as needed: thus for those groups whose cells contain no wireless nodes, no memory will be allocated. With these in mind, if you open the sparse grid Wireless Domain Model, the comments saved in the Wireless Domain Model editor, should make more sense. The full_grid and sparse_grid are examples of physical wireless domains.Besides the OPNET product documentation, a good source of information about Wireless Domain Models is session 1527 from OPNETWORK 2004. The wireless domain in 1527 is an example of a logical wireless domain. In that case, the partition of the whole set of wireless nodes into disjoint sub-sets is not achieved by regionally dividing a rectangle in smaller rectangular cells, but is achieved by virtue of some attribute settings on the nodes. Thus, all nodes with a particular attribute setting will form one group, nodes with another setting will form another group etc.

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