Heavy-Traffic Optimal Size- and State-Aware Dispatching
Runhan Xie, Isaac Grosof, Ziv Scully
TL;DR
This work tackles the problem of minimizing mean delay in FCFS dispatching with size- and state-aware information. It introduces CARD, a threshold-based policy that purposely creates imbalance across FCFS queues and uses a medium-size class to regulate the short-queue workload, and it proves a universal lower bound on mean delay while showing CARD is heavy-traffic optimal and matches that bound as load approaches capacity. The analysis leverages drift-based arguments, rate conservation, Palm inversion, and below-above cycles to connect mean delay to a single critical constant $K_{CARD}$ and to bound CARD's performance across any number of servers. Simulations demonstrate CARD’s strong performance beyond heavy traffic, with variants like Flexible CARD and multi-band CARD offering substantial practical gains and competitive performance relative to Dice. Overall, CARD establishes a new benchmark for size- and state-aware dispatching in FCFS systems and provides a methodological toolkit for analyzing similar policies.
Abstract
Dispatching systems, where arriving jobs are immediately assigned to one of multiple queues, are ubiquitous in computer systems and service systems. A natural and practically relevant model is one in which each queue serves jobs in FCFS (First-Come First-Served) order. 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. A major obstacle is that no nontrivial lower bound on mean delay is known, even in heavy traffic (i.e. the limit as load approaches capacity). This makes it difficult to prove that any given policy is optimal, or even heavy-traffic optimal. In this work, we propose the first size- and state-aware dispatching policy that provably minimizes mean delay in heavy traffic. Our policy, called CARD (Controlled Asymmetry Reduces Delay), keeps all but one of the queues short, then routes as few jobs as possible to the one long queue. We prove an upper bound on CARD's mean delay, and we prove the first nontrivial lower bound on the mean delay of any size- and state-aware dispatching policy. Both results apply to any number of servers. Our bounds match in heavy traffic, implying CARD's heavy-traffic optimality. In particular, CARD's heavy-traffic performance improves upon that of LWL (Least Work Left), SITA (Size Interval Task Assignment), and other policies from the literature whose heavy-traffic performance is known.