Separation of timescales in a two-layered network

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traffic: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a fixed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.Comment: 8 pages, 2 figures, 1 table, ITC 24 (2012

Compact Markov-modulated models for multiclass trace fitting

Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes

Validity of heavy traffic steady-state approximations in generalized Jackson Networks

We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether the stationary distribution of RBM provides a valid approximation for the steady-state of the original network. In this paper we resolve this open problem by proving that the re-scaled stationary distribution of the GJN converges to the stationary distribution of the RBM, thus validating a so-called ``interchange-of-limits'' for this class of networks. Our method of proof involves a combination of Lyapunov function techniques, strong approximations and tail probability bounds that yield tightness of the sequence of stationary distributions of the GJN.Comment: Published at http://dx.doi.org/10.1214/105051605000000638 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Towards Autonomic Service Provisioning Systems

This paper discusses our experience in building SPIRE, an autonomic system for service provision. The architecture consists of a set of hosted Web Services subject to QoS constraints, and a certain number of servers used to run session-based traffic. Customers pay for having their jobs run, but require in turn certain quality guarantees: there are different SLAs specifying charges for running jobs and penalties for failing to meet promised performance metrics. The system is driven by an utility function, aiming at optimizing the average earned revenue per unit time. Demand and performance statistics are collected, while traffic parameters are estimated in order to make dynamic decisions concerning server allocation and admission control. Different utility functions are introduced and a number of experiments aiming at testing their performance are discussed. Results show that revenues can be dramatically improved by imposing suitable conditions for accepting incoming traffic; the proposed system performs well under different traffic settings, and it successfully adapts to changes in the operating environment.Comment: 11 pages, 9 Figures, http://www.wipo.int/pctdb/en/wo.jsp?WO=201002636

Workload Prediction for Efficient Performance Isolation and System Reliability

In large-scaled and distributed systems, like multi-tier storage systems and cloud data centers, resource sharing among workloads brings multiple benefits while introducing many performance challenges. The key to effective workload multiplexing is accurate workload prediction. This thesis focuses on how to capture the salient characteristics of the real-world workloads to develop workload prediction methods and to drive scheduling and resource allocation policies, in order to achieve efficient and in-time resource isolation among applications. For a multi-tier storage system, high-priority user work is often multiplexed with low-priority background work. This brings the challenge of how to strike a balance between maintaining the user performance and maximizing the amount of finished background work. In this thesis, we propose two resource isolation policies based on different workload prediction methods: one is a Markovian model-based and the other is a neural networks-based. These policies aim at, via workload prediction, discovering the opportune time to schedule background work with minimum impact on user performance. Trace-driven simulations verify the efficiency of the two pro- posed resource isolation policies. The Markovian model-based policy successfully schedules the background work at the appropriate periods with small impact on the user performance. The neural networks-based policy adaptively schedules user and background work, resulting in meeting both performance requirements consistently. This thesis also proposes an accurate while efficient neural networks-based pre- diction method for data center usage series, called PRACTISE. Different from the traditional neural networks for time series prediction, PRACTISE selects the most informative features from the past observations of the time series itself. Testing on a large set of usage series in production data centers illustrates the accuracy (e.g., prediction error) and efficiency (e.g., time cost) of PRACTISE. The superiority of the usage prediction also allows a proactive resource management in the highly virtualized cloud data centers. In this thesis, we analyze on the performance tickets in the cloud data centers, and propose an active sizing algorithm, named ATM, that predicts the usage workloads and re-allocates capacity to work- loads to avoid VM performance tickets. Moreover, driven by cheap prediction of usage tails, we also present TailGuard in this thesis, which dynamically clones VMs among co-located boxes, in order to efficiently reduce the performance violations of physical boxes in cloud data centers

Integration of reliable algorithms into modeling software

In this note we discuss strategies that would enhance modern modeling and simulation software (MSS) with reliable routines using validated data types, controlled rounding, algorithmic differentiation and interval equation or initial value problem solver. Several target systems are highlighted. In stochastic traffic modeling, the computation of workload distributions plays a prominent role since they influence the quality of service parameters. INoWaTIV is a workload analysis tool that uses two different techniques: the polynomial factorization approach and the Wiener-Hopf factorization to determine the work-load distributions of GI/GI/1 and SMP/GI/1 service systems accurately. Two extensions of a multibody modeling and simulation software were developed to model kinematic and dynamic properties of multibody systems in a validated way. Furthermore, an interface was created that allows the computation of convex hulls and reliable lower bounds for the distances between subpav-ing-encoded objects constructed with SIVIA (Set Inverter Via Interval Analysis)

The effect of workload dependence in systems: Experimental evaluation, analytic models, and policy development

This dissertation presents an analysis of performance effects of burstiness (formalized by the autocorrelation function) in multi-tiered systems via a 3-pronged approach, i.e., experimental measurements, analytic models, and policy development. This analysis considers (a) systems with finite buffers (e.g., systems with admission control that effectively operate as closed systems) and (b) systems with infinite buffers (i.e., systems that operate as open systems).;For multi-tiered systems with a finite buffer size, experimental measurements show that if autocorrelation exists in any of the tiers in a multi-tiered system, then autocorrelation propagates to all tiers of the system. The presence of autocorrelated flows in all tiers significantly degrades performance. Workload characterization in a real experimental environment driven by the TPC-W benchmark confirms the existence of autocorrelated flows, which originate from the autocorrelated service process of one of the tiers. A simple model is devised that captures the observed behavior. The model is in excellent agreement with experimental measurements and captures the propagation of autocorrelation in the multi-tiered system as well as the resulting performance trends.;For systems with an infinite buffer size, this study focuses on analytic models by proposing and comparing two families of approximations for the departure process of a BMAP/MAP/1 queue that admits batch correlated flows, and whose service time process may be autocorrelated. One approximation is based on the ETAQA methodology for the solution of M/G/1-type processes and the other arises from lumpability rules. Formal proofs are provided: both approximations preserve the marginal distribution of the inter-departure times and their initial correlation structures.;This dissertation also demonstrates how the knowledge of autocorrelation can be used to effectively improve system performance, D_EQAL, a new load balancing policy for clusters with dependent arrivals is proposed. D_EQAL separates jobs to servers according to their sizes as traditional load balancing policies do, but this separation is biased by the effort to reduce performance loss due to autocorrelation in the streams of jobs that are directed to each server. as a result of this, not all servers are equally utilized (i.e., the load in the system becomes unbalanced) but performance benefits of this load unbalancing are significant