Optimal Placement of Spare Modules in a Cascaded Chain

A class of redundant cascaded chains with i.i.d. modules is considered in which recovery from a failure takes place by replacing the faulty module by a spare module. The complexity of the reconfiguration process depends upon the location of spare modules in the cascade. This paper deals with the question of optimally placing the spare modules in order to minimize the s-expected recovery time (down time) of the system. Exact analysis is carried out for cascades with one and two spare modules and an approximate analysis is given for three or more spares. Even though exact analysis does not seem to be practical in the general case, the symmetry of spare module positions in the special cases discussed here and linearity of the system suggest that one might expect the optimal positions to be symmetric in general. Because of this symmetry, one can reduce the number of variables to be considered in the general case, however, some inaccuracies might be introduced.