No abstract

A central question in designing server farms today is how to efficiently provision the number of servers to extract the best performance under unpredictable demand patterns while not wasting energy. While one would like to turn servers off when they become idle to save energy, the large setup cost (both, in terms of setup time and energy penalty) needed to switch the server back on can adversely affect performance. The problem is made more complex by the fact that today's servers provide multiple sleep or standby states which trade off the setup cost with the power consumed while the server is 'sleeping'. With so many controls, finding the optimal server farm management policy is an almost intractable problem -How many servers should be on at any given time, how many should be off, and how many should be in some sleep state? In this paper, we employ the popular metric of Energy-Response time Product (ERP) to capture the energy-performance tradeoff, and present the first theoretical results on the optimality of server farm management policies. For a stationary demand pattern, we prove that there exists a very small, natural class of policies that always contains the optimal policy for a single server, and conjecture it to contain a near-optimal policy for multi-server systems. For time-varying demand patterns, we propose a simple, traffic-oblivious policy and provide analytical and empirical evidence for its near-optimality.

Join the Shortest Queue (JSQ) is a popular routing policy for server farms. However, until now all analysis of JSQ has been limited to First-Come-First-Serve (FCFS) server farms, whereas it is known that web server farms are better modeled as Processor Sharing (PS) server farms. We provide the first approximate analysis of JSQ in the PS server farm model for general job size distributions, obtaining the distribution of queue length at each queue. To do this, we approximate the queue length of each queue in the server farm by a one-dimensional Markov chain, in a novel fashion. We also discover some interesting insensitivity properties for PS server farms with JSQ routing, and discuss the near-optimality of JSQ.

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.

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan and Weiss (2009). Customers and servers play symmetrical roles. There are finite sets C and S of customer and server classes, respectively. Time is discrete and at each time step one customer and one server arrive in the system according to a joint probability measure μ on C× S, independently of the past. Also, at each time step, pairs of matched customers and servers, if they exist, depart from the system. Authorized matchings are given by a fixed bipartite graph (C, S, E⊂ C × S). A matching policy is chosen, which decides how to match when there are several possibilities. Customers/servers that cannot be matched are stored in a buffer. The evolution of the model can be described by a discrete-time Markov chain. We study its stability under various admissible matching policies, including ML (match the longest), MS (match the shortest), FIFO (match the oldest), RANDOM (match uniformly), and PRIORITY. There exist natural necessary conditions for stability (independent of the matching policy) defining the maximal possible stability region. For some bipartite graphs, we prove that the stability region is indeed maximal for any admissible matching policy. For the ML policy, we prove that the stability region is maximal for any bipartite graph. For the MS and PRIORITY policies, we exhibit a bipartite graph with a non-maximal stability region.