Statistical Behaviors of Distributed Transition Planning

The transition planning problem is to move a system from an existing starting configuration to a desired final configuration at the lowest possible cost. Prior work shows that the transition planning problem can be reduced to a bipartite matching problem and the stable marriage algorithm can be used to approximate a minimum cost transition in a distributed environment. In this paper, we study the efficiency of this mapping, including its best-case, worst-case, and statistical behavior. We discuss the relationship between algorithm performance and the distribution of the input data. We show that while there are cases in which this algorithm performs poorly, works well when the costs of transitioning between distributed resources follow a normal distribution. We discuss the applicability of this algorithm to real-world situations in which resources are thus distributed.