Heavy-Tailed Limits for Medium Size Jobs and Comparison Scheduling

We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS) and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a customer arriving in stationarity is smaller than exactly k>=0 out of the preceding m>=k arrivals. Then, conditioning on the preceding event, the sojourn time distribution of this newly arriving customer behaves asymptotically the same as if the customer were served in isolation with a server of rate (1-\rho)/(k+1) for PS/FBPS, and (1-\rho) for SRPT, respectively, where \rho is the traffic intensity. Hence, the introduced notion of conditional limits allows us to distinguish the asymptotic performance of the studied schedulers by showing that SRPT exhibits considerably better asymptotic behavior for relatively smaller jobs than PS/FBPS. Inspired by the preceding results, we propose an approximation to the SRPT discipline based on a novel adaptive job grouping mechanism that uses relative size comparison of a newly arriving job to the preceding m arrivals. Specifically, if the newly arriving job is smaller than k and larger than m-k of the previous m jobs, it is routed into class k. Then, the classes of smaller jobs are served with higher priorities using the static priority scheduling. The good performance of this mechanism, even for a small number of classes m+1, is demonstrated using the asymptotic queueing analysis under the heavy-tailed job requirements. We also discuss refinements of the comparison grouping mechanism that improve the accuracy of job classification at the expense of a small additional complexity.Comment: 26 pages, 2 figure

Scheduling for today’s computer systems: bridging theory and practice

Scheduling is a fundamental technique for improving performance in computer systems. From web servers to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers. In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems. The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time and provide results characterizing the distribution of response time and the fairness of scheduling policies. These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs

ARM Wrestling with Big Data: A Study of Commodity ARM64 Server for Big Data Workloads

ARM processors have dominated the mobile device market in the last decade due to their favorable computing to energy ratio. In this age of Cloud data centers and Big Data analytics, the focus is increasingly on power efficient processing, rather than just high throughput computing. ARM's first commodity server-grade processor is the recent AMD A1100-series processor, based on a 64-bit ARM Cortex A57 architecture. In this paper, we study the performance and energy efficiency of a server based on this ARM64 CPU, relative to a comparable server running an AMD Opteron 3300-series x64 CPU, for Big Data workloads. Specifically, we study these for Intel's HiBench suite of web, query and machine learning benchmarks on Apache Hadoop v2.7 in a pseudo-distributed setup, for data sizes up to $20GB$ files, $5M$ web pages and $500M$ tuples. Our results show that the ARM64 server's runtime performance is comparable to the x64 server for integer-based workloads like Sort and Hive queries, and only lags behind for floating-point intensive benchmarks like PageRank, when they do not exploit data parallelism adequately. We also see that the ARM64 server takes $\frac{1}{3}^{rd}$ the energy, and has an Energy Delay Product (EDP) that is $50-71\%$ lower than the x64 server. These results hold promise for ARM64 data centers hosting Big Data workloads to reduce their operational costs, while opening up opportunities for further analysis.Comment: Accepted for publication in the Proceedings of the 24th IEEE International Conference on High Performance Computing, Data, and Analytics (HiPC), 201

Aggregate matrix-analytic techniques and their applications

The complexity of computer systems affects the complexity of modeling techniques that can be used for their performance analysis. In this dissertation, we develop a set of techniques that are based on tractable analytic models and enable efficient performance analysis of computer systems. Our approach is three pronged: first, we propose new techniques to parameterize measurement data with Markovian-based stochastic processes that can be further used as input into queueing systems; second, we propose new methods to efficiently solve complex queueing models; and third, we use the proposed methods to evaluate the performance of clustered Web servers and propose new load balancing policies based on this analysis.;We devise two new techniques for fitting measurement data that exhibit high variability into Phase-type (PH) distributions. These techniques apply known fitting algorithms in a divide-and-conquer fashion. We evaluate the accuracy of our methods from both the statistics and the queueing systems perspective. In addition, we propose a new methodology for fitting measurement data that exhibit long-range dependence into Markovian Arrival Processes (MAPs).;We propose a new methodology, ETAQA, for the exact solution of M/G/1-type processes, (GI/M/1-type processes, and their intersection, i.e., quasi birth-death (QBD) processes. ETAQA computes an aggregate steady state probability distribution and a set of measures of interest. E TAQA is numerically stable and computationally superior to alternative solution methods. Apart from ETAQA, we propose a new methodology for the exact solution of a class of GI/G/1-type processes based on aggregation/decomposition.;Finally, we demonstrate the applicability of the proposed techniques by evaluating load balancing policies in clustered Web servers. We address the high variability in the service process of Web servers by dedicating the servers of a cluster to requests of similar sizes and propose new, content-aware load balancing policies. Detailed analysis shows that the proposed policies achieve high user-perceived performance and, by continuously adapting their scheduling parameters to the current workload characteristics, provide good performance under conditions of transient overload

Space sharing job scheduling policies for parallel computers

The distinguishing characteristic of space sharing parallel job scheduling policies is that applications are allocated non-overlapping processor subsets. The interference among jobs is reduced, the synchronization delays and message latencies can be predictable, and distinct processors may be allocated to cooperating processes so as to avoid the overhead of context switches associated with traditional time-multiplexing;The processor allocation strategy, the job selection criteria, and workload characteristics are fundamental factors that influence system performance under space sharing. Allocation can be static or dynamic. The processor subset allocated to an application is fixed under static space sharing, whereas it can change during execution under dynamic space sharing. Static allocation can produce more predictable run times, permits a wide range of compiler optimizations (e.g., static data distribution and binding), and avoids the processor releases and reallocations associated with dynamic allocation. Its major problem is that it can induce high processor fragmentation;In this dissertation, alternative static and dynamic space sharing policies that differ in the allocation discipline and the job selection criteria are studied. The results show that significantly superior performance can be achieved under static space sharing if applications can be folded (i.e., allocated fewer processors than they requested). Folding typically increases program efficiency and can reduce processor fragmentation. Policies that increase folding with the system load are proposed and compared to schemes that use unconstrained folding, no folding, and fixed maximum folding factors. The adaptive policies produced higher and more stable system utilization, significantly shorter mean response times, and good fairness curves. However, unconstrained folding resulted in considerably more severe processor fragmentation than no folding. Its advantage is that it exploits the efficiency improvement that typically results when an application is allocated fewer processors. Consequently, it can produce shorter mean response times than no folding under medium to heavy loads;Also because of this efficiency improvement, dynamic policies that reduce waiting times by executing a large number of jobs simultaneously are more promising than schemes that limit the number of active jobs. However, limiting the number of active applications can be the superior approach when folding does not improve application efficiency