We Are Impatient: Algorithms for Geographically Distributed Load   Balancing with (Almost) Arbitrary Load Functions
  In geographically-distributed systems, communication latencies are non-negligible. The perceived processing time of a request is thus composed of the time needed to route the request to the server and the true processing time. Once a request reaches a target server, the processing time depends on the total load of that server; this dependency is described by a load function. We consider a broad class of load functions; we just require that they are convex and two times differentiable. In particular our model can be applied to heterogeneous systems in which every server has a different load function. This approach allows us not only to generalize results for queuing theory and for batches of requests, but also to use empirically-derived load functions, measured in a system under stress-testing. The optimal assignment of requests to servers is communication-balanced, i.e. for any pair of non perfectly-balanced servers, the reduction of processing time resulting from moving a single request from the overloaded to underloaded server is smaller than the additional communication latency. We present a centralized and a decentralized algorithm for optimal load balancing. We prove bounds on the algorithms' convergence. To the best of our knowledge these bounds were not known even for the special cases studied previously (queuing theory and batches of requests). Both algorithms are any-time algorithms. In the decentralized algorithm, each server balances the load with a randomly chosen peer. Such algorithm is very robust to failures. We prove that the decentralized algorithm performs locally-optimal steps. Our work extends the currently known results by considering a broad class of load functions and by establishing theoretical bounds on the algorithms' convergence. These results are applicable for servers whose characteristics under load cannot be described by a standard mathematical models. 
Piotr Skowron and Krzysztof Rzadca
cs.DC