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

Markovian Workload Characterization for QoS Prediction in the Cloud.

Resource allocation in the cloud is usually driven by performance predictions, such as estimates of the future incoming load to the servers or of the quality-of-service (QoS) offered by applications to end users. In this context, characterizing web workload fluctuations in an accurate way is fundamental to understand how to provision cloud resources under time-varying traffic intensities. In this paper, we investigate the Markovian Arrival Processes (MAP) and the related MAP/MAP/1 queueing model as a tool for performance prediction of servers deployed in the cloud. MAPs are a special class of Markov models used as a compact description of the time-varying characteristics of workloads. In addition, MAPs can fit heavy-tail distributions, that are common in HTTP traffic, and can be easily integrated within analytical queueing models to efficiently predict system performance without simulating. By comparison with trace-driven simulation, we observe that existing techniques for MAP parameterization from HTTP log files often lead to inaccurate performance predictions. We then define a maximum likelihood method for fitting MAP parameters based on data commonly available in Apache log files, and a new technique to cope with batch arrivals, which are notoriously difficult to model accurately. Numerical experiments demonstrate the accuracy of our approach for performance prediction of web systems. © 2011 IEEE

Fitting procedure for the two-state Batch Markov modulated Poisson process

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which has been proposed for the modeling of dependent events occurring in batches (as group arrivals, failures or risk events). This paper focuses on exploring the possibilities of the \bmmpp for the modeling of real phenomena involving point processes with group arrivals. The first result in this sense is the characterization of the two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of moments related to the inter-event time and batch size distributions. This characterization leads to a sequential fitting approach via a moments matching method. The performance of the novel fitting approach is illustrated on both simulated and a real teletraffic data set, and compared to that of the EM algorithm. In addition, as an extension of the inference approach, the queue length distributions at departures in the queueing system BMMPP/M/1 is also estimated

Fitting procedure for the two-state Batch Markov modulated Poisson process

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which has been proposed for the modeling of dependent events occurring in batches (as group arrivals, failures or risk events). This paper focuses on exploring the possibilities of the BMMPP for the modeling of real phenomena involving point processes with group arrivals. The first result in this sense is the characterization of the two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of moments related to the inter-event time and batch size distributions. This characterization leads to a sequential fitting approach via a moments matching method. The performance of the novel fitting approach is illustrated on both simulated and a real teletraffic data set, and compared to that of the EM algorithm. In addition, as an extension of the inference approach, the queue length distributions at departures in the queueing system BMMPP/M/1 is also estimated

Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement. Implementation difficulties are also addressed with a focus on dealing with large data sets, where latent models are especially advantageous due the large number of observations facilitating identification of hidden factors. Namely, computational issues such as numerical underflow and high processing cost arise in this context and in this paper, we produce procedures to overcome these problems. This modelling framework is demonstrated using a large insurance data set to illustrate theoretical, practical and computational contributions and an empirical comparison to other count models highlight the advantages of the proposed approach.Comment: For simulated data sets and code, please go to https://github.com/agi-lab/reserving-MMNP

The search for QoS in data networks : A statistical approach

New Internet services like video on-demand, high definition IPTV, high definition video conferences and some real time applications have strong QoS requirements regarding losses, delay, jitter, etc. This work addresses the challenge of guaranteeing quality of service (QoS) in the Internet from a statistical point of view. Three lines of work are proposed. The first one is about the estimation of the QoS parameters from traffic traces (in the context of large deviation theory and effective bandwidth). The second one, address the admission control problem from results of the many sources and small buffer asymptotic. Finally, the third line focuses on the estimation of QoS parameters seen by an application based on end-to-end active measurements and statistical learning tool

Model-Driven System Capacity Planning under Workload Burstiness

In this paper, we define and study a new class of capacity planning models called MAP queueing networks. MAP queueing networks provide the first analytical methodology to describe and predict accurately the performance of complex systems operating under bursty workloads, such as multi-tier architectures or storage arrays. Burstiness is a feature that significantly degrades system performance and that cannot be captured explicitly by existing capacity planning models. MAP queueing networks address this limitation by describing computer systems as closed networks of servers whose service times are Markovian Arrival Processes (MAPs), a class of Markov-modulated point processes that can model general distributions and burstiness. In this paper, we show that MAP queueing networks provide reliable performance predictions even if the service processes are bursty. We propose a methodology to solve MAP queueing networks by two state space transformations, which we call Linear Reduction (LR) and Quadratic Reduction (QR). These transformations dramatically decrease the number of states in the underlying Markov chain of the queueing network model. From these reduced state spaces, we obtain two classes of bounds on arbitrary performance indexes, e.g., throughput, response time, utilizations. Numerical experiments show that LR an QR bounds achieve good accuracy. We also illustrate the high effectiveness of the LR and QR bounds in the performance analysis of a real multi-tier architecture subject to TPC-W workloads that are characterized as bursty. These results promote MAP queueing networks as a new robust class of capacity planning models

Fitting simulation input models for correlated traffic data

The adequate representation of input models is an important step in building valid simulation models. Modeling independent and identically distributed data is well established in simulation, but for some application areas like computer and communication networks it is known, that the assumption of independent and identically distributed data is violated in practice and that for example interarrival times or packet sizes exhibit autocorrelation over a large number of lags. Moreover, it is known that negligence of these correlations can result in a serious loss of validity of the simulation model. Although different stochastic processes, which can model these autocorrelations, like e.g. Autoregressive-To-Anything (ARTA) processes and Markovian Arrival Processes (MAPs), have been proposed in the past and more recently fitting algorithms to set the parameters of these processes such that they resemble the behavior of observations from a real system have been developed, the integration of correlated processes into simulation models is still a challenge. In this work ARTA processes are extended in several ways to account for the requirements when simulating models of computer and communication systems. In a first step ARTA processes are extended to use an Autoregressive Moving Average (ARMA) process instead of a pure Autoregressive (AR) base process to be able to capture a large number of autocorrelation lags, while keeping the model size small. In a second step they are enabled to use the flexible class of acyclic Phase-type distributions as marginal distribution. To support the usage of these novel processes in simulation models a fitting algorithm is presented, software for fitting and simulating these processes is developed and the tools are integrated into the toolkit ProFiDo, which provides a complete framework for fitting and analyzing different stochastic processes. By means of synthetically generated and real network traces it is shown that the presented stochastic processes are able to provide a good approximation of the marginal distribution as well as the correlation structure of the different traces and result in a compact process description

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