Blocking Probabilities for a Class of Spiderweb Channel Graphs

The blocking probabilities for spiderweb channel graphs are well known to be difficult to compute. Recently, Takagi studied a class of spiderweb channel graphs and gave recursive equations for computing their blocking probabilities. In this paper we use a recent result in combinatorics to give a dosed form solution for the recursive equations. Consequently, the blocking probability for any graph in this class can be expressed in a form involving at most two nested summations.