In this paper we study two fully-dynamic multi-dimensional vector load balancing problems with recourse. The adversary presents a stream of n job insertions and deletions, where each job j is a vector in ℝ^d_{≥ 0}. In the vector scheduling problem, the algorithm must maintain an assignment of the active jobs to m identical machines to minimize the makespan (maximum load on any dimension on any machine). In the vector bin packing problem, the algorithm must maintain an assignment of active jobs into a number of bins of unit capacity in all dimensions, to minimize the number of bins currently used. In both problems, the goal is to maintain solutions that are competitive against the optimal solution for the active set of jobs, at every time instant. The algorithm is allowed to change the assignment from time to time, with the secondary objective of minimizing the amortized recourse, which is the average cardinality of the change of the assignment per update to the instance. For the vector scheduling problem, we present two simple algorithms. The first is a randomized algorithm with an O(1) amortized recourse and an O(log d/log log d) competitive ratio against oblivious adversaries. The second algorithm is a deterministic algorithm that is competitive against adaptive adversaries but with a slightly higher competitive ratio of O(log d) and a per-job recourse guarantee bounded by Õ(log n + log d log OPT). We also prove a sharper instance-dependent recourse guarantee for the deterministic algorithm. For the vector bin packing problem, we make the so-called small jobs assumption that the size of all jobs in all the coordinates is O(1/log d) and present a simple O(1)-competitive algorithm with O(log n) recourse against oblivious adversaries. For both problems, the main challenge is to determine when and how to migrate jobs to maintain competitive solutions. Our central idea is that for each job, we make these decisions based only on the active set of jobs that are "earlier" than this job in some ordering ≺ of the jobs.

In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The goal is to find an online matching which minimizes the total cost, i.e., the sum of distances between each client and the server it is matched to. We know deterministic algorithms~\cite{KP93,khuller1994line} that achieve a competitive ratio of $2k-1$, and this bound is tight for deterministic algorithms. The problem has also long been considered in specialized metrics such as the line metric or metrics of bounded doubling dimension, with the current best result on a line metric being a deterministic $O(\log k)$ competitive algorithm~\cite{raghvendra2018optimal}. Obtaining (or refuting) $O(\log k)$-competitive algorithms in general metrics and constant-competitive algorithms on the line metric have been long-standing open questions in this area. In this paper, we investigate the robustness of these lower bounds by considering the Online Metric Matching with Recourse problem where we are allowed to change a small number of previous assignments upon arrival of a new client. Indeed, we show that a small logarithmic amount of recourse can significantly improve the quality of matchings we can maintain. For general metrics, we show a simple \emph{deterministic} $O(\log k)$-competitive algorithm with $O(\log k)$-amortized recourse, an exponential improvement over the $2k-1$ lower bound when no recourse is allowed. We next consider the line metric, and present a deterministic algorithm which is $3$-competitive and has $O(\log k)$-recourse, again a substantial improvement over the best known $O(\log k)$-competitive algorithm when no recourse is allowed.

Volatile resources are surplus cloud resources not consumed by high priority foreground (reserved/on-demand) load. These resources are exploited by a growing number of users. Today, cloud operators provide no statistical characterization of volatile resources. We consider how releasing such statistics could improve user value by studying Amazon's 608 EC2 Spot Instance types. Results show that as little as two parameters such as (average, 90pctile) can increase user value by 30%. These results are robust over four-fifths (475 of 608) of instance types. Beyond competitive concerns, cloud operators are reluctant to share volatile resource statistics because they might be considered a service-level agreement (SLA), and thus constrain their ability to serve foreground load. We show that clever resource management can allay such concerns. We study two plausible classes of foreground load changes, showing one class where such a concern is indeed valid and another where it is not. We design two online resource management algorithms that detect foreground load variation and adapt to maintain a statistical SLA. The algorithms not only improve the ability to maintain guarantees and user value but also improve user experience, reducing job failures by 50%. These results apply to the Stable and Transition classes of instance types, which account for nearly all of the instance types (577 of 608).

Motivated by the problem of packing Virtual Machines on physical servers in the cloud, we study the problem of online stochastic bin packing under two settings -- packing with permanent items, and packing under item departures. In the setting with permanent items, we present the first truly distribution-oblivious bin packing heuristic that achieves O(√n) regret compared to OPT for all distributions. Our algorithm is essentially gradient descent on suitably defined Lagrangian relaxation of the bin packing Linear Program. We also prove guarantees of our heuristic against non i.i.d. input using a randomly delayed Lyapunov function to smoothen the input.

We present a new tool to analyze three queueing systems which have defied exact analysis so far: (i) the classical M/G/k multi-server system, (ii) queueing systems with fluctuating arrival and service rates, and (iii) the M/G/1 round-robin queue. We argue that rather than looking for exact expressions for the mean response time as a function of the job size distribution, a more fruitful approach is to find distributions which minimize or maximize the mean response time given the first n moments of the job size distribution.

Power-proportional cluster-based storage is an important component of an overall cloud computing infrastructure. With it, substantial subsets of nodes in the storage cluster can be turned off to save power during periods of low utilization. Rabbit is a distributed file system that arranges its data-layout to provide ideal power-proportionality down to very low minimum number of powered-up nodes (enough to store a primary replica of available datasets). Rabbit addresses the node failure rates of large-scale clusters with data layouts that minimize the number of nodes that must be powered-up if a primary fails. Rabbit also allows different datasets to use different subsets of nodes as a building block for interference avoidance when the infrastructure is shared by multiple tenants. Experiments with a Rabbit prototype demonstrate its power-proportionality, and simulation experiments demonstrate its properties at scale.

The delivery of video content is expected to gain huge momentum, fueled by the popularity of user-generated clips, growth of VoD libraries, and wide-spread deployment of IPTV services with features such as CatchUp/PauseLive TV and NPVR capabilities. The `time-shifted' nature of these personalized applications defies the broadcast paradigm underlying conventional TV networks, and increases the overall bandwidth demands by orders of magnitude. Caching strategies provide an effective mechanism for mitigating these massive bandwidth requirements by replicating the most popular content closer to the network edge, rather than storing it in a central site. The reduction in the traffic load lessens the required transport capacity and capital expense, and alleviates performance bottlenecks. In the present paper, we develop light-weight cooperative cache management algorithms aimed at maximizing the traffic volume served from cache and minimizing the bandwidth cost. As a canonical scenario, we focus on a cluster of distributed caches, either connected directly or via a parent node, and formulate the content placement problem as a linear program in order to benchmark the globally optimal performance. Under certain symmetry assumptions, the optimal solution of the linear program is shown to have a rather simple structure. Besides interesting in its own right, the optimal structure offers valuable guidance for the design of low-complexity cache management and replacement algorithms. We establish that the performance of the proposed algorithms is guaranteed to be within a constant factor from the globally optimal performance, with far more benign worst-case ratios than in prior work, even in asymmetric scenarios. Numerical experiments for typical popularity distributions reveal that the actual performance is far better than the worst-case conditions indicate.