Consider a dense string topology network, where the number of nodes N ? ?, as shown in Figure 4.6. Analytically estimate the fractional locations of p 1 and p 2 by considering the following scenario: the source node s is situated at the left side of point p 1 (as shown in the figure), and all communications are meant for the destination node, which is located at the fractional location 1.0 (i.e., at the extreme end) of the dense string.
This is a challenge problem. One of the possible approaches can be considered as follows: Add
two LLs located at (f1, f2) and (g1, g2). The positions of those LLs can be arranged in five
ways: (06f1 < f2, f1 < f26g1), (06f1 < g1, g16f2 < g2), (g16f1 < f2, f1 < f26g2), (g1 < f162, g2 < f26 1), and (g26f1 < f2,f1 < f26 1).
Now, for each case, derive the shortest path expression as mentioned in Appendix C in the textbook. When shortest path
values related to all possible LL-connecting locations are evaluated, the optimal location of
the two concurrent LLs will be the minimum of all shortest path possibilities.
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