Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 13

Consider the M × N rectangular grid of computer stations shown in Fig. 13.57, where the spacing between stations is d. Assume these stations are to be connected by a star- configured LAN using the duct network shown in the figure. Furthermore, assume that each station is connected to the central star by means of its own dedicated cable.
( a ) If m and n denote the relative position of the star, show that the total cable length L needed to connect the stations is given by
L = [ MN ( M + N + 2)/2 Nm
× ( M m + 1) Mn ( N n + l)] d
( b ) Show that if the star is located in one corner of the grid, then this expression becomes
L = MN ( M + N 2) d /2
( c ) Show that the shortest cable length is obtained when the star is at the center of the grid.