The Blocking Probability of Spider-Web Networks
We determine the limiting behavior of the blocking probability for spider-web networks, a class of crossbar switching networks proposed by Ikeno. We use a probabilistic model proposed by the author, in which the busy links always form disjoint routes through the network. We show that if the occupancy probability is below the threshold 2 - √2 = 0.5857…, then the blocking probability tends to zero, whereas above this threshold it tends to one. This provides a theoretical explanation for results observed empirically in simulations by Bassalygo, Neiman, and Vvedenskaya.
© 1991 Wiley Periodicals, Inc., A Wiley Company
Pippenger, N. (1991), The blocking probability of spider-web networks. Random Struct. Alg., 2: 121–149. doi: 10.1002/rsa.3240020202