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. We present optimization centralized and a decentralized algorithms for 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 and self-stabilizing algorithms.