The Number of Rearrangements Performed via Extended Connection Chains for Rearrangeable Clos Networks

Various switching networks have been investigated because of their practical importance and theoretical interests. Among these networks, this study focuses on the Clos network. A Clos network is constructed by placing switches in three stages. In the first and third stages, r (r > 1) switches are aligned, whereas m (m > 1) switches are aligned in the second stage. There are n inputs and m outputs in the first stage. Symmetrically, the third stage switch has m inputs and n outputs. For this configuration, if n  m 2n  2, the network is rearrangeable. Though existing connections in a rearrangeable network may block a newly requested connection, the blocking is always removed by rerouting existing connections. An interesting problem arose during this process is how many existing connections must be rearranged: the number of rearrangements. Although the problem has been studied for a long time, the number of rearrangements is not completely clarified for arbitrary combinations of parameters m, n, and r. This study presents a new upper bound on the number of rearrangements for 2  n m 2n  2 . This bound is derived from the extended connection chain concept proposed in a previous study. Using this concept, the paper first derives from the case where a parameter, s, represents the load on a second-stage switch. Then, the paper presents another new upper bound, which is independent of parameter s. The study shows that the presented upper bound is smaller than the previously known bounds for a certain range of m.

SMM Clos-Network Switches under SD Algorithm

This paper is devoted to evaluating the performance of Space-Memory-Memory (SMM) Clos-network switches under a packet dispatching scheme employing static connection patterns, referred to as Static Dispatching (SD). The control algorithm with static connection patterns can be easily implemented in the SMM fabric due to bufferless switches in the first stage. Stability is one of the very important performance factors of packet switching nodes. In general, a switch is stable for a particular arrival process if the expected length of the packet queues does not increase without limitation. To prove the stability of the SMM Clos-network switches considered under the SD packet dispatching scheme the discrete Markov chain model of the switch is used and Foster’s criteria to extend Lyapunov’s second (direct) method of stability investigation of discrete time stochastic systems are used. The results of simulation experiments, in terms of average cell delay and packet queue lengths, are shown as well.

Rearrangeability of 2×2 W-S-W Elastic Switching Fabrics with Two Connection Rate

The rearreangeable conditions for the 2×2 three-stage switching fabric of a W-S-W architecture for elastic optical switches are considered in this paper. Analogies between the switching fabric considered and the three-stage Clos network are shown. On the other hand, differences are also shown, which presented the modifications required in the control algorithm used in rearrangeable networks. The rearrangeable conditions and the control algorithm are presented and proved. Operation of the proposed control algorithm is shown based on a few examples. The required number of frequency slot units in interstage links of rearrangeable switching fabrics is much lower than in the strict-sense non-blocking switching fabrics characterized by the same parameters.