Rearrangeable Clos networks have been studied for a long time due to their many applications, as well as their theoretical interest. In a rearrangeable Clos network, a newly requested connection may be blocked by existing connections. However, this blocking is eliminated by adequately rearranging some other existing connections. In this operation, an interesting topic is the sufficient number of rearrangements required to eliminate the blocking. Despite previous studies, the sufficient number of rearrangements has only been found for limited cases and has not been completely determined for generic parameter values. This paper analyses the number of rearrangements using the connection chain concept, which clearly and efficiently represents a sequence of connections to be rearranged. The analysis assumes the employment of a rearrangement algorithm, which eliminates the blocking using the shortest connection chain. The usage of the shortest connection chain results in the minimum number of rearrangements. As a result, this paper determines a new bound on the number of rearrangements for a parameter range that has not been considered in any previous studies. In addition, this paper examines the condition for which the system is unblocked via one rearrangement.

可重排Clos网络由于其许多应用以及其理论兴趣已被研究了很长时间。在可重排的Clos网络中，新请求的连接可能会被现有连接阻止。但是，通过适当地重新布置一些其他现有的连接，可以消除这种阻塞。在此操作中，一个有趣的话题是消除阻塞所需的足够数量的重新排列。尽管有先前的研究，但仅在有限的情况下才发现足够数量的重排，而对于通用参数值尚未完全确定。本文使用连接链概念分析了重新排列的次数，该概念清楚有效地表示了要重新排列的连接顺序。分析假设采用了重排算法，使用最短的连接链可以消除阻塞。使用最短的连接链可以减少重新排列的次数。结果，本文为先前研究中未曾考虑过的参数范围的重排数目确定了新的界限。此外，本文还研究了通过一次重排来解除系统阻塞的情况。