Utility Optimal Thread Assignment and Resource Allocation in Multi-Server Systems

Achieving high performance in many multi-server systems requires finding a good assignment of worker threads to servers and also effectively allocating each server's resources to its assigned threads. The assignment and allocation components of this problem have been studied extensively but largely separately in the literature. In this paper, we introduce the assign and allocate (AA) problem, which seeks to simultaneously find an assignment and allocation that maximizes the total utility of the threads. Assigning and allocating the threads together can result in substantially better overall utility than performing the steps separately, as is traditionally done. We model each thread by a utility function giving its performance as a function of its assigned resources. We first prove that the AA problem is NP-hard. We then present a $2 (\sqrt{2}-1) > 0.828$ factor approximation algorithm for concave utility functions, which runs in $O(mn^2 + n (\log mC)^2)$ time for $n$ threads and $m$ servers with $C$ amount of resources each. We also give a faster algorithm with the same approximation ratio and $O(n (\log mC)^2)$ time complexity. We then extend the problem to two more general settings. First, we consider threads with nonconcave utility functions, and give a 1/2 factor approximation algorithm. Next, we give an algorithm for threads using multiple types of resources, and show the algorithm achieves good empirical performance. We conduct extensive experiments to test the performance of our algorithms on threads with both synthetic and realistic utility functions, and find that they achieve over 92\% of the optimal utility on average. We also compare our algorithms with a number of practical heuristics, and find that our algorithms achieve up to 9 times higher total utility.