Algorithmic Approaches to Reducing Resource Costs in Data Centers

Title of dissertation: ALGORITHMIC APPROACHES TO REDUCING RESOURCE COSTS IN DATA CENTERS Koyel Mukherjee, Doctor of Philosophy, 2013 Dissertation directed by: Professor Samir Khuller Department of Computer Science A substantial portion of resource costs incurred by data centers relate to energy costs, with cooling energy and equipment powering energy accounting for a major fraction. Other major costs incurred by data centers, is due to huge data transmission volume and resultant network bandwidth consumption. In this dissertation, we study problems inspired by the needs to reduce energy consumption and network bandwidth billing costs in data centers. A significant amount of data center cooling energy is wasted due to thermal imbalance and hot spots. In order to prevent hot spots, it is desirable to schedule the workload in a data center in a thermally aware manner, assigning jobs to machines not just based on local load of the machines, but based on the overall thermal profile of the data center. This is challenging because of the spatial cross-interference between machines, where a job assigned to a machine may impact not only that machine’s temperature, but also nearby machines due to directional cooling mechanisms currently used in most data centers and subsequent hot air recirculation effects. We define the notion of effective load of a machine, that captures this effect and analyze several different models for two natural (both strongly NP-hard) optimization problems: 1) maximizing the profit of scheduled jobs under a cooling energy budget, and a resultant maximum temperature limit; 2) minimizing the maximum temperature on any machine while scheduling all jobs. For the first problem, we give a 1 2 −O( ) approximation for profit maximization on all three models. For the second problem we give a 2 approximation offline algorithm and a 3 competitive online algorithm for a single rack of machines, where the approximation factor approaches 4 3 and the competitive ratio approaches 2, respectively as the cross-interference falls off. The analysis of all these algorithms is tight. Apart from cooling issues, servers consume energy while running; hence, shutting down some will reduce energy consumption. In this context, we consider two problems that have been studied in the literature: 1) the active time problem and 2) the busy time problem, The goal in both cases is to minimize the total time the machines are ‘on’, however, in the active time model, we have access to a single machine whereas in the busy time model we have access to unlimited number of machines. The machines have bounded capacity and the jobs have release times, deadlines and arbitrary processing lengths. For the active time problem, we give a 3 approximation algorithm for non-unit length jobs with integral preemption and show our analysis is tight. We give a 2 approximation algorithm via LP rounding, and also show that the integrality gap of the LP is 2. For the busy time model, we give a 3 approximation algorithm which improves the best known result of 4. We consider the preemptive problem as well and give new algorithms. Data centers need to transmit a huge volume of data every day, and the resultant network bandwidth consumption costs are extremely high. Frequently, Internet Service Providers charge for Internet use either based on the peak bandwidth usage in any slot in a billing cycle, or according to a percentile (often the 95th percentile) cost model. As a result, an enterprise could save on billing costs by optimizing these measures by delaying some traffic, if possible. However, in reality, traffic is of different types, where some cannot be delayed, and some traffic (such as ftp, bulk data transfer) can be delayed. We provide an optimal offline algorithm for the percentile problem when jobs can have variable delay. We also consider the online problem of minimizing the maximum bandwidth. There exists a tight e-competitive online algorithm for the general problem, where the delay allowed for certain jobs can be arbitrarily large and time is considered to be continuous. We consider smaller values of delay and discrete time slots, since in practice we may not want to delay traffic too much. We give new lower bounds, which are much better than e, on the competitive ratio of online algorithms for several values of delay, and propose and analyze online algorithms with better upper bounds than e for small delay. ALGORITHMIC APPROACHES TO REDUCING RESOURCE COSTS IN DATA CENTERS