Heavy-Traffic Optimal Size- and State-Aware Dispatching

We study the problem of dispatching jobs to multiple FCFS (First-Come, First-Served) queues. We consider the case where the dispatcher is size-aware, meaning it learns the size (i.e. service time) of each job as it arrives; and state-aware, meaning it always knows the amount of work (i.e. total remaining service time) at each queue. While size- and state-aware dispatching to FCFS queues has been extensively studied, little is known about optimal dispatching for the objective of minimizing mean delay. In this work, we propose the first size- and state-aware dispatching policy, called CARD (Controlled Asymmetry Reduces Delay), that provably minimizes mean delay in heavy traffic. This work summarizes our full paper.