Andrew J. Rindos

Exact Methods for the Transient Analysis of Nonhomogeneous Continuous Time Markov Chains

Most common performance and reliability models assume that rates associated with events such as arrivals, service completions, failures, repairs, etc. are all constant in time. Many practical systems, however, require time- (age-) dependent rates. For example, the use of Weibull failure rates is quite common in many reliability models. Likewise, most actual local area network (LAN) systems experience surges in the number of users that vary in magnitude over time. These surges may often be approximated by a periodic process. Therefore, nonhomogeneous continuous time Markov chains (CTMCs) may be well suited to model such systems. The transient analysis of time-varying linear systems is highly advanced in the field of systems and control theory. We present a review of some useful results, and then apply them to the analysis of nonhomogeneous CTMCs (especially periodic ones). One of the results of this analysis is, that for a certain class of useful nonhomogeneous CTMCs, a very simple method exists for transforming such a CTMC (and not just a periodic one) to an equivalent homogeneous CTMC that is then amenable to such homogeneous methods as Jensen’s method (also known as uniformization or randomization).

Techniques and tools for reliability and performance evaluation: problems and perspectives

Modelling techniques and tools of the future must meet the challenges presented by todays highly demanding and schedule-oriented developing environment. With the emergence of high performance and reliability systems the problem of how to analyze such systems has become increasingly more difficult. Traditional assumptions of independent events, exponential distributions and other such “convenient” assumptions no longer model systems realistically. Nevertheless, the demand for answering performance and reliability related questions during the design process has increased. In this paper we discuss some of the issues involved in integrating modeling and design during a product development process. We present a broad range of existing techniques of systems analysis. We also describe a variety of tools that have been developed to make the analysis process simpler.

Gigabit Ethernet PCI adapter performance

We analyze the performance of a commercially available Gigabit Ethernet adapter, using TCP/IP running on a Windows NT operating system. We show how the performance varies with number of clients, sessions per client, number of system processors, and speed of system processors. Throughout, we discuss how the Ethernet protocol, adapter hardware, operating system, and device driver interact to produce the throughput results measured, and suggest ways to improve performance.

Achieving and assuring high availability

We discuss availability aspects of large software-based systems. We classify faults into Bohrbugs, Mandelbugs and aging-related bugs, and then examine mitigation methods for the last two bug types. We also consider quantitative approaches to availability assurance.

Resiliency Quantification for Large Scale Systems: An IaaS Cloud Use Case

We quantify the resiliency of large scale systems upon changes encountered beyond the normal system behavior. General steps for resiliency quantification are shown and resiliency metrics are defined to quantify the effects of changes. The proposed approach is illustrated through an Infrastructure- as-a-Service (IaaS) Cloud use case. Specifically, we assess the impact of changes in demand and available capacity on the Cloud resiliency using interacting state-space based sub- models where interdependencies are resolved using fixed- point iteration. Since, resiliency quantification involves un- derstanding the transient behavior of the system, fixed-point variables evolve with time leading to non-homogenous Markov chains. In this paper, we present an algorithm for resiliency analysis when dealing with such non-homogenous sub-models. A comparison is shown with our past research, where we quantified the resiliency of IaaS Cloud performance using a one level monolithic model. Numerical results show that the approach proposed in this paper can scale for a real sized Cloud without significantly compromising the accuracy.

An Approach for Resiliency Quantification of Large Scale Systems

We quantify the resiliency of large scale systems upon changes encountered beyond the normal system behavior. Formal definitions for resiliency and change are provided together with general steps for resiliency quantification and a set of resiliency metrics that can be used to quantify the effects of changes. A formalization of the approach is also shown in the form of a set of four algorithms that can be applied when large scale systems are modeled through stochastic analytic state space models (monolithic models or interacting sub-models). In particular, in the case of interacting submodels, since resiliency quantification involves understanding the transient behavior of the system, fixed-point variables evolve with time leading to non-homogenous Markov chains. At the best of our knowledge, this is the first paper facing this problem in a general way. The proposed approach is applied to an Infrastructure-as-a-Service (IaaS) Cloud use case. Specifically, we assess the impact of changes in demand and available capacity on the Cloud resiliency and we show that the approach proposed in this paper can scale for a real sized Cloud without significantly compromising the accuracy.

Innovation within IBM (and WebSphere) development through university collaborations

Historically over the years, IBM has supported a wide array of university relations programs, at the corporate, business unit/product division and local (geographical) levels. These programs have been used to support a variety of objectives that include: product innovation, testing, proof-of-concepts and showcases; talent development and recruiting; sales opportunities; corporate citizenship and visibility; and others. An effective application of these university relations resources and programs occurs within the Chief Technology Offices (CTOs) of several IBM Software Group (SWG) product divisions. A notable example is WebSphere CTO, and specifically its Emerging Technology Institute (ETI), which defines the new products, new features, new technologies etc. for the IBM WebSphere product portfolio. It maintains a pair of regional university relations centers, the Centers for Advanced Studies (CAS), located in Research Triangle Park, North Carolina (US) and Toronto (Canada), which are also co-located at two of WebSpheres largest product development sites. These centers work directly with the local universities in support of product innovation and (student) talent development and recruitment, and are part of a larger network of some 26 such centers located around the world. This talk will provide an overview of the various IBM corporate university relations programs that are managed by the Global University Programs (GUP) team. These include the IBM Shared University Relations (SUR) program, the IBM Faculty Awards and Innovation Awards programs, the IBM PhD Fellowship program, the Open Collaborative Research (OCR) program and many others. It will also provide an overview of other special programs within IBM that support educational and research institutions, including the Academic Initiative, the Systems and Technology Group (STG) University Alliances, Corporate Citizen and Corporate Affairs (CCCA) and many others. An overview of the CAS program, together with the structure of IBM university relations world wide from country to country, will be provided. It will presented in a context that demonstrates how the 26 CAS programs and numerous local country university relations teams leverage these programs to maintain a strong partnership with local academia, while driving innovation within IBM products and services development. This talk will conclude with an outstanding example of how RTP CAS, IBM university relations and IBM hardware development partnered with a local university to develop a revolutionary cloud computing solution, the Virtual Computing Lab (VCL) developed at NC State University in Raleigh NC.

ATM to the desktop

Over the last 2 to 3 years, ATM has emerged as the strategic technology for the WAN and the LAN environments. This paper will explore ATMs capabilities in the LAN and in particular as a desktop connectivity technology. Because of its bandwidth scalability, ATM can accommodate the various bandwidth needs of desktop client and server platforms from 25 to 155 to 622 Mbps. New and emerging desktop applications like videoconferencing, network- based education, and multimedia applications require the isochronous capabilites of ATM. This paper will focus on application requirements on the desktop and how ATM meets those requirements, along with migration strategies from legacy ALNs to ATM. Costs and timing for desktop migration to ATM are discussed.

Transient Analysis of Nonhomogeneous Continuous Time Markov Chains Describing Realistic LAN Systems

Most actual local area network (LAN) systems experience surges in the number of users that vary in magnitude over time. In addition, these surges may often be approximated by a periodic process (with a period of one day or one week). Therefore, a nonhomogeneous continuous time Markov chain (CTMC) may be the best model for such a system, at least for those periods of the day when these surges vary rapidly in magnitude. The transient analysis of time-varying linear systems is highly advanced in the field of systems and control theory. We present a review of some useful results, and then apply them to the analysis of nonhomogeneous CTMCs (especially periodic ones). One of the results of this analysis is a very simple method for transforming any nonhomogeneous CTMC (not just a. periodic one) to an equivalent homogeneous CTMC that is then amenable to such homogeneous methods as uniformization. We also present what we feel is a more realistic transient model for the discrete changes in user population that are observed.

Approximate Computation of Sojourn Time Distribution in Open Queueing Networks

The method of decomposition of queues has been widely used in solution of large and complex queueing networks for which exact solutions do not exist. We apply the basic paradigm of decomposition in computing approximations to the sojourn-time distribution in open queueing networks in which the service times and arrival processes are non-Markovian. For doing so we have made use of existing results on sojourn time distribution at a single queue. Using these, a queueing network is translated into a semi-Markov chain, whose absorption time distribution approximates the sojourn time distribution of the queueing network. However, the semi-Markov model does not represent the state of the queueing network (i.e., number of jobs at each queue). The state-space size of the semi-Markov models is thus linear in the number of queues in the network. This is achieved by having one state in the semi-Markov model corresponding to each queue in the queueing network, and one absorbing state to denote exit out of the network. The states are then connected together according to the topology of the network. The holding time distribution of a state is the sojourn time distribution at the corresponding queue. This sojourn time distribution must be computed by considering each queue in isolation. We approximate the arrival process to each queue to a phase-type arrival process, and then compute the sojourn time distribution assuming it is a PH/G/1 queue. Once we have the holding time distributions and the routing probability matrix, the absorption time distribution of the semi-Markov chain can be computed. The absorption time distribution approximates the sojourn time distribution of the queueing network.