Consider a service system where incoming tasks are instantaneously dispatched to one out of many heterogeneous server pools. Associated with each server pool is a concave utility function which depends on the class of the server pool and its current occupancy. We derive an upper bound for the mean normalized aggregate utility in stationarity and introduce two load balancing policies that achieve this upper bound in a large-scale regime. Furthermore, the transient and stationary behavior of these asymptotically optimal load balancing policies is characterized on the scale of the number of server pools, in the same large-scale regime.

翻译：考虑一个服务系统，其中到达的任务被即时分配至多个异构服务器池之一。每个服务器池关联一个凹效用函数，该函数取决于服务器池的类别及其当前占用率。我们推导了稳态下归一化平均总效用的上界，并引入了两种在大规模场景下达到该上界的负载均衡策略。此外，在相同的大规模场景下，这些渐近最优负载均衡策略的瞬态与稳态行为也依据服务器池数量的规模进行了刻画。