Constrained Load-Balancing Policies for Parallel Single-Server Queue Systems

Flow-control policies that balance server loads are well known for improving performance of queueing systems with multiple nodes. However, although load balancing benefits the system overall, it may negatively impact some of the queueing nodes. For example, it may reduce throughput rates or engender unfairness with respect to some performance measures. For queueing systems with multiple single-server nodes, we propose a set of constrained load-balancing policies that ensures the expected arrival rate to each queueing node is not reduced, and we show that such policies provide multiple benefits for each queueing node: stochastically fewer customers and lower variance of the number of customers at each queueing node. These results imply performance improvement as measured by multiple general objective functions, including but not limited to the expected number of customers at a queueing node, probability of having a high number of customers, variance of the number of customers, and expected number of customers conditional on exceeding a threshold defined by a fixed service level. We demonstrate numerically that our proposed policies capture a large portion of the potential maximal improvement.