1 research outputs found
Heavy-Traffic Optimal Size- and State-Aware Dispatching
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.Comment: ACM SIGMETRICS / IFIP Performance 202