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

The pseudo-self-similar traffic model: application and validation

Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems

Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues

In modern computer systems, workload varies at different times and locations. It is important to model the performance of such systems via workload models that are both representative and efficient. For example, model-generated workloads represent realistic system behaviour, especially during peak times, when it is crucial to predict and address performance bottlenecks. In this thesis, we model performance, namely throughput and delay, using adaptive models and discrete queues. Hidden Markov models (HMMs) parsimoniously capture the correlation and burstiness of workloads with spatiotemporal characteristics. By adapting the batch training of standard HMMs to incremental learning, online HMMs act as benchmarks on workloads obtained from live systems (i.e. storage systems and financial markets) and reduce time complexity of the Baum-Welch algorithm. Similarly, by extending HMM capabilities to train on multiple traces simultaneously it follows that workloads of different types are modelled in parallel by a multi-input HMM. Typically, the HMM-generated traces verify the throughput and burstiness of the real data. Applications of adaptive HMMs include predicting user behaviour in social networks and performance-energy measurements in smartphone applications. Equally important is measuring system delay through response times. For example, workloads such as Internet traffic arriving at routers are affected by queueing delays. To meet quality of service needs, queueing delays must be minimised and, hence, it is important to model and predict such queueing delays in an efficient and cost-effective manner. Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal levels. We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling. Further, we propose a dynamic strategy of service allocation to minimise delays in UDP traffic flows whilst maximising a utility function.Open Acces

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

Statistical Analysis and Modeling of SIP Traffic for Parameter Estimation of Server Hysteretic Overload Control, Journal of Telecommunications and Information Technology, 2013, nr 4

The problem of overload control in Session Initiation Protocol (SIP) signaling networks gives rise to many questions which attract researchers from theoretical and practical point of view. Any mechanism that is claimed to settle this problem down demands estimation of local (control) parameters on which its performance is greatly dependent. In hysteretic mechanism these parameters are those which define hysteretic loops. In order to find appropriate values for parameters one needs adequate model of SIP traffic flow circulating in the network under consideration. In this paper the attempt is made to address this issue. Analysis of SIP traffic collected from telecommunication operator’s network is presented. Traffic profile is built. It is shown that fitting with Markov Modulated Poisson Process with more than 2 phases is accurate. Estimated values of its parameters are given

Dependence-driven techniques in system design

Burstiness in workloads is often found in multi-tier architectures, storage systems, and communication networks. This feature is extremely important in system design because it can significantly degrade system performance and availability. This dissertation focuses on how to use knowledge of burstiness to develop new techniques and tools for performance prediction, scheduling, and resource allocation under bursty workload conditions.;For multi-tier enterprise systems, burstiness in the service times is catastrophic for performance. Via detailed experimentation, we identify the cause of performance degradation on the persistent bottleneck switch among various servers. This results in an unstable behavior that cannot be captured by existing capacity planning models. In this dissertation, beyond identifying the cause and effects of bottleneck switch in multi-tier systems, we also propose modifications to the classic TPC-W benchmark to emulate bursty arrivals in multi-tier systems.;This dissertation also demonstrates how burstiness can be used to improve system performance. Two dependence-driven scheduling policies, SWAP and ALoC, are developed. These general scheduling policies counteract burstiness in workloads and maintain high availability by delaying selected requests that contribute to burstiness. Extensive experiments show that both SWAP and ALoC achieve good estimates of service times based on the knowledge of burstiness in the service process. as a result, SWAP successfully approximates the shortest job first (SJF) scheduling without requiring a priori information of job service times. ALoC adaptively controls system load by infinitely delaying only a small fraction of the incoming requests.;The knowledge of burstiness can also be used to forecast the length of idle intervals in storage systems. In practice, background activities are scheduled during system idle times. The scheduling of background jobs is crucial in terms of the performance degradation of foreground jobs and the utilization of idle times. In this dissertation, new background scheduling schemes are designed to determine when and for how long idle times can be used for serving background jobs, without violating predefined performance targets of foreground jobs. Extensive trace-driven simulation results illustrate that the proposed schemes are effective and robust in a wide range of system conditions. Furthermore, if there is burstiness within idle times, then maintenance features like disk scrubbing and intra-disk data redundancy can be successfully scheduled as background activities during idle times

HetHetNets: Heterogeneous Traffic Distribution in Heterogeneous Wireless Cellular Networks

A recent approach in modeling and analysis of the supply and demand in heterogeneous wireless cellular networks has been the use of two independent Poisson point processes (PPPs) for the locations of base stations (BSs) and user equipments (UEs). This popular approach has two major shortcomings. First, although the PPP model may be a fitting one for the BS locations, it is less adequate for the UE locations mainly due to the fact that the model is not adjustable (tunable) to represent the severity of the heterogeneity (non-uniformity) in the UE locations. Besides, the independence assumption between the two PPPs does not capture the often-observed correlation between the UE and BS locations. This paper presents a novel heterogeneous spatial traffic modeling which allows statistical adjustment. Simple and non-parameterized, yet sufficiently accurate, measures for capturing the traffic characteristics in space are introduced. Only two statistical parameters related to the UE distribution, namely, the coefficient of variation (the normalized second-moment), of an appropriately defined inter-UE distance measure, and correlation coefficient (the normalized cross-moment) between UE and BS locations, are adjusted to control the degree of heterogeneity and the bias towards the BS locations, respectively. This model is used in heterogeneous wireless cellular networks (HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic on the network performance. This network is called HetHetNet since it has two types of heterogeneity: heterogeneity in the infrastructure (supply), and heterogeneity in the spatial traffic distribution (demand).Comment: JSA

Packet dropping characteristics in a queue with autocorrelated arrivals

This paper provides a detailed description of the packet dropping process connected with the buffer overflows in a network node. Namely, we show the formulas for the most important loss characteristics, both in the transient and the stationary regime and then illustrate them via numericalexamples. In order to make it possible to obtain the droppingcharacteristics for strongly autocorrelated arrivals, the Markovmodulated Poisson process is used as a traffic model