Algorithms for the State Probabilities in a General Class of Single Server Queueing Systems with Group Arrivals

Performance evaluation methods that have been used so far failed to capture the real characteristics of network traffic. This is especially true when the service times are general such as the variable bit rate (VBR) video, which is proven to be self-similar. In the paper, diffusion approximation methods are proposed to analyse a dynamic scheduler for self-similar VBR video traffic in asynchronous transfer mode (ATM) networks. The proposed scheme employs a coupled queueing system that has been used extensively in the modelling of computer and communication systems. Diffusion approximations methods are used to decouple a queueing system which represents an ATM network node into separate G/G/1 queues. Real MPEG video traces are used in the discrete event simulation. Results are compared with the approximation, and are found to work very well under different traffic conditions.

This paper presents a unifying algorithmic analysis for a general class of single server queueing systems with a state dependent Markovian input process and a phase-type service time distribution including single server queues with random and quasirandom input. Using regenerative analysis we develop numerically stable and efficient recursion schemes to compute the state probabilities. The computation of the waiting times is based on the state probabilities.

For a single server queue with state dependent Markovian input and state dependent general service times we give a stable recursive algorithm to compute the steady-state probabilities. An integral representation of the coefficients in the recursive scheme is given. For service time distributions of phase type the computation of the coefficients simplifies considerably in that only matrix-vector operations are needed and no integrations.

In this paper we discuss the performance analysis of a single server queue with Poisson arrivals and arbitrary service times which are conditioned on the number of customers (units) in the system at the beginning of the service of a customer. The system has a finite capacity K. The model is denoted by M/Gn/K, and has wide applications in computer-communication systems. An algorithm has been developed to compute the steady-state probabilities at departure and arbitrary epochs. Numerical results have been presented for various special cases: two-state service rates; two-state mixed service; and many-state service rates. The algorithm is computationally efficient, accurate and reliable for both high and low values of the model parameters and works for all the service time distributions including the non-phase type. Some comparative studies have been presented in the form of tables and graphs.

This book covers techniques that can be used to analyze data from IoT sensors and addresses questions regarding the performance of an IoT system. It strikes a balance between practice and theory so one can learn how to apply these tools in practice with a good understanding of their inner workings. This is an introductory book for readers who have no familiarity with these techniques. The techniques presented in An Introduction to IoT Analytics come from the areas of machine learning, statistics, and operations research. Machine learning techniques are described that can be used to analyze IoT data generated from sensors for clustering, classification, and regression. The statistical techniques described can be used to carry out regression and forecasting of IoT sensor data and dimensionality reduction of data sets. Operations research is concerned with the performance of an IoT system by constructing a model of the system under study and then carrying out a what-if analysis. The book also describes simulation techniques. Key Features IoT analytics is not just machine learning but also involves other tools, such as forecasting and simulation techniques. Many diagrams and examples are given throughout the book to fully explain the material presented. Each chapter concludes with a project designed to help readers better understand the techniques described. The material in this book has been class tested over several semesters. Practice exercises are included with solutions provided online at www.routledge.com/9780367686314 Harry G. Perros is a Professor of Computer Science at North Carolina State University, an Alumni Distinguished Graduate Professor, and an IEEE Fellow. He has published extensively in the area of performance modeling of computer and communication systems.

We first consider a wide class of single-server queues with state dependent Markovian input including the finite capacity M/G/1 queue and the machine repair problem. We specify efficient and stable algorithms to compute the steady-state probabilities and the moments of the waiting time. Next we discuss the multi-server queue with Poisson input and general service times. We present for the steady-state probabilities good quality approximations to be computed from a stable recursive algorithm. As a by-product we obtain simple approximations for the delay probability and the moments of the waiting time. For the output process we derive tractable and good approximations for the moments of the interdeparture time. Also we discuss extensions to the finite capacity M/G/c queue and the machine repair problem with multiple repairmen having general repair times.

A novel flexible discipline for providing priority in a single-server queue is applied to the system where the service can be unreliable what results in the loss of a customer or repetition of its service. According to this discipline, arriving customers are stored in the finite buffers dedicated to the customers of the corresponding type if the buffer is not full. After the staying in the corresponding buffer during the exponentially distributed time, the customers try to enter the main buffer of a finite capacity which is common for both types of customers. If this main buffer is full, the customer returns to the dedicated buffer and repeats the attempts to enter the main buffer later. Customers staying in the dedicated buffers are impatient and can go away from the system after a certain patience period duration of which has an exponential distribution. Customers of both types, which succeed to enter the main buffer, are picked up for the service in the order of their admission to this buffer. Providing the preference to priority customers is managed via the corresponding choice of capacities of the dedicated buffers and the rate of trials to transfer to the main buffer. Performance measures of this system are obtained under the assumption that the arrival flows of two types of customers are defined by the Markov arrival processes and the service time has the distribution of phase-type with failures type. Some aspects relating to an optimal choice of the parameters of the system are discussed via numerical experiments.

This chapter presents many real-life examples modeled using MOSEL. Many of these examples, which cover practical modeling of computer, communication and manufacturing systems, are results of recent publications.

In this paper we examine certain problems related to the use of diffusion approximations for the approximate modelling of computer systems. In particular we develop a model which allows us to handle waiting times and batch arrivals: these results are a new approach to the use of diffusion approximations. We also examine the effect of the distribution of holding times at boundaries: this question had remained open in earlier studies. We show that the stationary distributions associated with these diffusion models depend only on the average residence time of the process on the boundaries and not on the complete distribution function. This result justifies the use of exponential holding times as had been done in an earlier study.

Tandem queues are good mathematical models for description of information transmission in various communication systems and networks. These queues play also an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, their investigation is interesting for theory and applications. In this paper, we consider tandem queue suitable for modeling the systems and networks where information flows are correlated and bursty what is typical for many modern telecommunication networks. Possible correlation of customers inter-arrival times and batch arrivals are taken into account via of consideration of the Batch Markovian Arrival Process (BMAP) as input stream to the system. The system consists of two stations. The service time at the station 1 is assumed to be generally distributed. There is no buffer at this station, and customers who meet the busy server repeat attempts to enter the system in random time intervals. The service process at the station 2 is assumed to be described by the continuous time Markov chain with a finite state space. This assumption holds good, e.g., if the station 2 has a finite buffer, consists of a finite number of identical or heterogeneous servers where the service time distribution is assumed to be of PH (PHase) type. Markov chain embedded at service completion epochs at the station 1 and the process of system states at arbitrary time are under study. Ergodicity condition and algorithms for computing the steady state probabilities are presented.

A novel retrial multi-server queueing model with batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of a batch arrive one-by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival process. Batch size distribution is geometric. The number of batches, which can be admitted into the system simultaneously, is subject of control. Analysis of the joint distribution of the number batches and customers in the system is implemented using the tool of the multi-dimensional asymptotically quasi-Toeplitz Markov chains.

The five papers in this special issue are based on a selection of top theoretical papers from the ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, which took place at Austin, Texas, in June 2014. As the premier conference on the measurement and modeling of computer systems, the technical program featured papers that covered both theory and applications from a wide variety of areas, including algorithms, communication networks, dynamics and control, optimization, performance analysis, resource allocation and scheduling, and stochastic modeling, among others. The program consisted of 40 papers selected from more than 237 international submissions by a technical program committee of well-established researchers from all over the world. We seek with this special issue to highlight some of the recent theoretical work on the mathematical analysis and modeling of computer systems. The paper of Larranaga, Ayesta, and Verloop deals with a resource allocation problem in a multi-class server with convex holding costs and user impatience under the average cost criterion. Although the optimal policy has a complex dependency on all the input parameters and state information, the authors derive simple index policies obtained by solving a relaxed version of the optimal stochastic control problem and combining results from restless multi-armed bandits and queueing theory.

This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams.This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

In this paper, we develop a Linearizer-type approximation technique for the analysis of large multiple-chain queueing networks that contain multi-server first-come, first-served queues with service times that are chain dependent. Use is made of a waiting time approximation based on Mean Value Analysis that has recently been developed by Souza e Silva and Muntz. The storage requirements of the iterative scheme are of the order of NR2, and the computational requirements are of the order of NR3, where N is the number of nodes and R is the number of closed routing chains. In comparing the results obtained with published empirical stress test results, the accuracy of the Linearizer-type approximation is found to be acceptable. An application in which the proposed iterative technique is found to be particularly useful is in the analysis of large queueing networks with nested passive resources and many closed routing chains, of the type arising in the modeling of computer systems with multi-programming constraints and of computer-communication networks with window flow controls.

Systems biology has arisen through the convergence of theoretical, computational, and mathematical modeling of systems and the need to understand the wealth of information being rapidly generated in biology. Systems biology by its nature requires collaborations between scientists with expertise in biology, chemistry, computer sciences, engineering, mathematics, and physics. Successful integration of these disciplines depends on bringing to bear both social and technological tools: namely, consortia that help forge collaborations and common understanding, software tools that permit analysis of vast and complex data, and agreed-upon standards that enable researchers to communicate and reuse each other's results in practical and unambiguous ways. In this presentation, I will discuss several international projects (SBML, SBGN, and BioModels.net) aimed at addressing the last issue.An important prerequisite for effective sharing of computational models is reaching agreement on how to communicate them, both between software and between humans. The Systems Biology Markup Language (SBML) project is an effort to create a machine-readable format for representing computational models at the biochemical reaction level. By supporting SBML as an input and output format, different software tools can operate on the same representation of a model, removing chance for errors in translation and assuring a common starting point for analyses and simulations. SBML has become the most successful effort in this direction so far, with nearly 100 software tools supporting it today.A recently-created sister project is the Systems Biology Graphical Notation (SBGN) project. It addresses the issue of consistent human communication, by attempting to add more rigor and consistency to the graphical network diagrams that often accompany published research on models of biological reaction systems. The real payoff will come when more people and software adopt such a common visual notation and it becomes as familiar to them as circuit schematics are to electronics engineers.Finally, when developing and publishing computational models, it is only natural to want to put them into a database. The BioModels.net project is an effort to (1) provide a free, centralized, publicly-accessible database of human-curated computational models in SBML and other structured formats; (2) define agreed-upon standards for model curation; and (2) define agreed-upon vocabularies for annotating models with connections to biological data resources.