A Steady State Analysis of Di ractingTreesNir

Diiracting trees are an eeective and highly scalable distributed-parallel technique for shared counting and load balancing. This paper presents the rst steady-state combinatorial model and analysis for diiracting trees, and uses it to answer several critical algorithmic design questions. Our model is simple and suuciently high level to overcome many implementation speciic 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 dii-racting tree algorithm and modify it to a create a more stable version. We are also able to identify the range in which the diiracting tree performs most eeciently, and the ranges in which its performance degrades. We believe our model and modeling approach open the way to steady-state analysis of other distributed-parallel structures such as counting networks and elimination trees.