Lachlan L. H. Andrew

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.

Power-Aware Speed Scaling in Processor Sharing Systems

Energy use of computer communication systems has quickly become a vital design consideration. One effective method for reducing energy consumption is dynamic speed scaling, which adapts the processing speed to the current load. This paper studies how to optimally scale speed to balance mean response time and mean energy consumption under processor sharing scheduling. Both bounds and asymptotics for the optimal speed scaling scheme are provided. These results show that a simple scheme that halts when the system is idle and uses a static rate while the system is busy provides nearly the same performance as the optimal dynamic speed scaling. However, the results also highlight that dynamic speed scaling provides at least one key benefit - significantly improved robustness to bursty traffic and mis-estimation of workload parameters.

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.

Connectivity, coverage and placement in wireless sensor networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes.

Understanding XCP: equilibrium and fairness

We prove that the XCP equilibrium solves a constrained max-min fairness problem by identifying it with the unique solution of a hierarchy of optimization problems, namely those solved by max-min fair allocation, but solved by XCP under an additional constraint. We describe an algorithm to compute this equilibrium and derive a lower and upper bound on link utilization. While XCP reduces to max-min allocation at a single link, in a network the additional constraint can cause a flow to receive an arbitrarily small fraction of its max-min allocation. We present simulation results to confirm our analytical findings.

MaxNet: a congestion control architecture for scalable networks

MaxNet is a distributed congestion control architecture. This paper analyzes the stability properties of MaxNet. We show that MaxNet is stable for networks with arbitrary delays, numbers of sources, capacities, and topologies. Unlike existing proposals, MaxNet does not need to estimate the number of bottleneck links on the end-to-end path to achieve these scaling properties.

Simple and Effective Dynamic Provisioning for Power-Proportional Data Centers

Energy consumption represents a significant cost in data center operation. A large fraction of the energy, however, is used to power idle servers when the workload is low. Dynamic provisioning techniques aim at saving this portion of the energy, by turning off unnecessary servers. In this paper, we explore how much gain knowing future workload information can bring to dynamic provisioning. In particular, we develop online dynamic provisioning solutions with and without future workload information available. We first reveal an elegant structure of the off-line dynamic provisioning problem, which allows us to characterize the optimal solution in a “divide-and-conquer” manner. We then exploit this insight to design two online algorithms with competitive ratios 2 - α and e/ (e - 1 + α), respectively, where 0 ≤ α ≤ 1 is the normalized size of a look-ahead window in which future workload information is available. A fundamental observation is that future workload information beyond the full-size look-ahead window (corresponding to α= 1) will not improve dynamic provisioning performance. Our algorithms are decentralized and easy to implement. We demonstrate their effectiveness in simulations using real-world traces.

Joint Allocation of Subcarriers and Transmit Powers in a Multiuser OFDM Cellular Network

In the present paper, we consider the problem of joint bandwidth (subcarriers) and power allocation for the downlink of a multi-user multi-cell OFDM cellular network. This resource allocation problem is formulated as a power minimization problem, subject to meeting the target rates of all users in the network. We develop a distributed solution to find the globally optimal allocation which determines the subcarrier and power allocation dynamically. In addition, we investigate the impact of reducing the complexity by reducing the number of degrees of freedom available in the optimization. In particular, we consider a static bandwidth allocation scheme, and a static power allocation scheme. The numerical results show that the penalty on network performance due to the reduction in the available degrees of freedom is not significant.

Optimal speed scaling under arbitrary power functions

This paper investigates the performance of online dynamic speed scaling algorithms for the objective of minimizing a linear combination of energy and response time. We prove that (SRPT, P--1 (n)), which uses Shortest Remaining Processing Time (SRPT) scheduling and processes at speed such that the power used is equal to the queue length, is 2-competitive for a very wide class of power-speed tradeoff functions. Further, we prove that there exist tradeoff functions such that no online algorithm can attain a competitive ratio less than 2.

Power-aware speed scaling in processor sharing systems: Optimality and robustness

Adapting the speed of a processor is an effective method to reduce energy consumption. This paper studies the optimal way to scale speed to balance response time and energy consumption under processor sharing scheduling. It is shown that using a static rate while the system is busy provides nearly optimal performance, but having a wider range of available speeds increases robustness to different traffic loads. In particular, the dynamic speed scaling optimal for Poisson arrivals is also constant-competitive in the worst case. The scheme that equates power consumption with queue occupancy is shown to be 10-competitive when power is cubic in speed.