Minghong Lin

Dynamic right-sizing for power-proportional data centers

Power consumption imposes a significant cost for data centers implementing cloud services, yet much of that power is used to maintain excess service capacity during periods of predictably low load. This paper investigates how much can be saved by dynamically ‘right-sizing’ the data center by turning off servers during such periods, and how to achieve that saving via an online algorithm. We prove that the optimal offline algorithm for dynamic right-sizing has a simple structure when viewed in reverse time, and this structure is exploited to develop a new ‘lazy’ online algorithm, which is proven to be 3-competitive. We validate the algorithm using traces from two real data center workloads and show that significant cost-savings are possible.

Online algorithms for geographical load balancing

It has recently been proposed that Internet energy costs, both monetary and environmental, can be reduced by exploiting temporal variations and shifting processing to data centers located in regions where energy currently has low cost. Lightly loaded data centers can then turn off surplus servers. This paper studies online algorithms for determining the number of servers to leave on in each data center, and then uses these algorithms to study the environmental potential of geographical load balancing (GLB). A commonly suggested algorithm for this setting is “receding horizon control” (RHC), which computes the provisioning for the current time by optimizing over a window of predicted future loads. We show that RHC performs well in a homogeneous setting, in which all servers can serve all jobs equally well; however, we also prove that differences in propagation delays, servers, and electricity prices can cause RHC perform badly, So, we introduce variants of RHC that are guaranteed to perform as well in the face of such heterogeneity. These algorithms are then used to study the feasibility of powering a continent-wide set of data centers mostly by renewable sources, and to understand what portfolio of renewable energy is most effective.

A tale of two metrics: simultaneous bounds on competitiveness and regret

We consider algorithms for “smoothed online convex optimization” (SOCO) problems, which are a hybrid between online convex optimization (OCO) and metrical task system (MTS) problems. Historically, the performance metric for OCO was regret and that for MTS was competitive ratio (CR). There are algorithms with either sublinear regret or constant CR, but no known algorithm achieves both simultaneously. We show that this is a fundamental limitation – no algorithm (deterministic or randomized) can achieve sublinear regret and a constant CR, even when the objective functions are linear and the decision space is one dimensional. However, we present an algorithm that, for the important one dimensional case, provides sublinear regret and a CR that grows arbitrarily slowly.

Heavy-traffic analysis of mean response time under shortest remaining processing time

Shortest Remaining Processing time (SRPT) has long been known to optimize the queue length distribution and the mean response time (a.k.a. flow time, sojourn time). As such, it has been the focus of a wide body of analysis. However, results about the heavy-traffic behavior of SRPT have only recently started to emerge. In this work, we characterize the growth rate of the mean response time under SRPT in the M/GI/1 system under general job size distributions. Our results illustrate the relationship between the job size tail and the heavy traffic growth rate of mean response time. Further, we show that the heavy traffic growth rate can be used to provide an accurate approximation for mean response time outside of heavy traffic regime.

The average response time in a heavy-traffic srpt queue

Shortest Remaining Processing Time first (SRPT) has long been known to optimize the queue length distribution and the mean response time (a.k.a. flow time, sojourn time). As such, it has been the focus of a wide body of analysis. However, results about the heavy-traffic behavior of SRPT have only recently started to emerge. In this work, we characterize the growth rate of the mean response time under SRPT in the M/GI/1 system under general job size distributions. Our results illustrate the relationship between the job size tail and the heavy traffic growth rate of mean response time. Further, we show that the heavy traffic growth rate can be used to provide an accurate approximation for mean response time outside of heavy traffic.