Comparisons on Blocking Probabilities for Regular Series Parallel Channel Graphs

Comparisons on Blocking Probabilities for Regular Series Parallel Channel Graphs By D. Z. Du and F. K. HWANG (Manuscript received January 19,1982) We give a sufficient condition for one regular series parallel channel graph to be superior to another with the same number of stages. The main mathematical tools used for doing this are the recently developed results on majorization over a partial order. I. INTRODUCTION An s-stage channel graph is a graph whose vertices can be partitioned into s subsets (stages) Vi, V2, · · · , Vs, with V and V8 each containing a single vertex (called the source and the sink, respectively), and whose edges can be partitioned into s -- 1 subsets Ei, E2, · · ·, Es-1 such that (i) Edges in Ei connect vertices in V, to vertices in Vi+i, (ii) Each vertex in V,, 1