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,即进入的任务即时发送到众多不同服务器库中的一个中。 与每个服务器库相关联的是一个集成公用功能,它取决于服务器库的级别及其目前的占用情况。 我们为平均正常的固定性总用电量设定了一个上限,并引入了两个负载平衡政策,在大规模系统中实现这一上限。 此外,这些无创意的最佳负载平衡政策的瞬时和固定行为以服务器库数量的规模为特征,在同一大规模系统中。