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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. 

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SRPT outperforms all existing scheduling policies for all loads, with improvements by orders of magnitude at higher loads. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known. 

The Gittins scheduling policy minimizes the mean response in the single-server M/G/1 queue in a wide variety of settings. Most famously, Gittins is optimal when preemption is allowed and service requirements are unknown but drawn from a known distribution. Gittins is also optimal much more generally, adapting to any amount of available information and any preemption restrictions. However, scheduling to minimize mean response time in a multiserver setting, specifically the central-queue M/G/k, is a much more difficult problem. In this work we give the first general analysis of Gittins in the M/G/k. Specifically, we show that under extremely general conditions, Gittins's mean response time in the M/G/k is at most its mean response time in the M/G/1 plus an $O(łog(1/(1 - ρ)))$ additive term, where ρ is the system load. A consequence of this result is that Gittins is heavy-traffic optimal in the M/G/k if the service requirement distribution S satisfies $\mathbfE [S^2(łog S)^+] < \infty$. This is the most general result on minimizing mean response time in the M/G/k to date. To prove our results, we combine properties of the Gittins policy and Palm calculus in a novel way. Notably, our technique overcomes the limitations of tagged job methods that were used in prior scheduling analyses. 

Web services rely on caching at nearly every layer of thesystem architecture. Commonly, each cache is implementedand maintained independently by a distinct team and is highlyspecialized to its function. For example, an application-datacache would be independent from a CDN cache. However, thisapproach ignores the difficult challenges that different cachingsystems have in common, greatly increasing the overall effortrequired to deploy, maintain, and scale each cache.This paper presents a different approach to cache devel-opment, successfully employed at Facebook, which extractsa core set of common requirements and functionality fromotherwise disjoint caching systems.CacheLibis a general-purpose caching engine, designed based on experiences witha range of caching use cases at Facebook, that facilitates theeasy development and maintenance of caches. CacheLib wasfirst deployed at Facebook in 2017 and today powers over 70services including CDN, storage, and application-data caches.This paper describes our experiences during the transitionfrom independent, specialized caches to the widespread adop-tion of CacheLib. We explain how the characteristics of pro-duction workloads and use cases at Facebook drove importantdesign decisions. We describe how caches at Facebook haveevolved over time, including the significant benefits seen fromdeploying CacheLib. We also discuss the implications our ex-periences have for future caching design and research.