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A steady state analysis of diffracting trees (extended abstract)

Dijj%-acting trees are an effective and highly scalable distributed-parallel technique for shared counting and load balancing. This paper presents the first steady-state combinatorial model and analysis for diffracting trees, and usesit to answer several critical algorithmic design questions. Our model is simple and sufficiently high level to overcome many implementation specific details, and yet as we will show it is rich enough to accurately predict empirically observed behaviors. As a result of our analysis we were able to identify starvation problems in the original diffracting tree algor~thm and modify it to a create a more stable version. We are also able to identify the range in which the diffracting tree performs most efficiently, and the rangesin which its performance degrades, We believe ourmodel and modeling approach open the way to steady-state analysis of other distributed-parallel structures such as counting networks and elimination trees.