A compensation approach for queueing problems

No abstract

Queueing networks: solutions and applications

During the pasttwo decades queueing network models have proven to be a versatile tool for computer system and computer communication system performance evaluation. This chapter provides a survey of th field with a particular emphasis on applications. We start with a brief historical retrospective which also servesto introduce the majr issues and application areas. Formal results for product form queuenig networks are reviewed with particular emphasis on the implications for computer systems modeling. Computation algorithms, sensitivity analysis and optimization techniques are among the topics covered. Many of the important applicationsof queueing networks are not amenableto exact analysis and an (often confusing) array of approximation methods have been developed over the years. A taxonomy of approximation methods is given and used as the basis for for surveing the major approximation methods that have been studied. The application of queueing network to a number of areas is surveyed, including computer system cpacity planning, packet switching networks, parallel processing, database systems and availability modeling.Durante as últimas duas décadas modelos de redes de filas provaram ser uma ferramenta versátil para avaliação de desempenho de sistemas de computação e sistemas de comunicação. Este capítulo faz um apanhado geral da área, com ênfase em aplicações. Começamos com uma breve retrospectiva histórica que serve também para introduzir os pontos mais importantes e as áreas de aplicação. Resultados formais para redes de filas em forma de produto são revisados com ênfase na modelagem de sistemas de computação. Algoritmos de computação, análise de sensibilidade e técnicas de otimização estão entre os tópicos revistos. Muitas dentre importantes aplicações de redes de filas não são tratáveis por análise exata e uma série (frequentemente confusa) de métodos de aproximação tem sido desenvolvida. Uma taxonomia de métodos de aproximação é dada e usada como base para revisão dos mais importantes métodos de aproximação propostos. Uma revisão das aplicações de redes de filas em um número de áreas é feita, incluindo planejamento de capacidade de sistemas de computação, redes de comunicação por chaveamento de pacotes, processamento paralelo, sistemas de bancos de dados e modelagem de confiabilidade

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems

Canonical approximation in the performance analysis of distributed systems

The problem of analyzing distributed systems arises in many areas of computer science, such as communication networks, distributed databases, packet radio networks, VLSI communications and switching mechanisms. Analysis of distributed systems is difficult since one must deal with many tightly-interacting components. The number of possible state configurations typically grows exponentially with the system size, making the exact analysis intractable even for relatively small systems. For the stochastic models of these systems, whose steady-state probability is of the product form, many global performance measures of interest can be computed once one knows the normalization constant of the steady-state probability distribution. This constant, called the system partition function, is typically difficult to derive in closed form. The key difficulty in performance analysis of such models can be viewed as trying to derive a good approximation to the partition function or calculate it numerically. In this Ph.D. work we introduce a new approximation technique to analyze a variety of such models of distributed systems. This technique, which we call the method of Canonical Approximation, is similar to that developed in statistical physics to compute the partition function. The new method gives a closed-form approximation of the partition function and of the global performance measures. It is computationally simple with complexity independent of the system size, gives an excellent degree of precision for large systems, and is applicable to a wide variety of problems. The method is applied to the analysis of multihop packet radio networks, locking schemes in database systems, closed queueing networks, and interconnection networks

Probabilistic Performance Testing of Web Applications

IT süsteemid muutuvad oma elutsükli vältel järjest keerulisemaks. Veebirakendusi kasutatakse eriti laialt erinevatel eesmärkidel, sest võrgupõhine juurdepääs informatsioonile on väga mugav. Kuid võrgupõhise juurdepääsu juures tekivad mõned probleemid, mida tuleks silmas pidada. Kasutajad eeldavad prognoositavat jõudlust (nt nõuetekohane reaktsiooniaeg), seega teenusepakkujad peavad teadma, kuidas nende süsteem töötab erinevate koormuste all. Selles teesis loome tõhususe analüütilise mudeli ja töötame välja programmi, mis selle lahendab. Antud programm lubab analüüsida veebirakenduste jõudlust ja vastata järgmistele küsimustele: 1)missugune on keskmine süsteemi reaktsiooniaeg? 2)missugune on süsteemi kasutamine üldiselt? Parameetrid programmi jaoks nagu keskmine teenindusaeg, uute taotluste keskmine saabumisaeg, keskmine mõtlemisaeg, on saadud testsüsteemi reaalse koormuse logidest. Jõudluse mudel on välja töötatud Queuing Networksi abil, mis lubab analüüsida süsteemi matemaatiliste valemite abil.Web systems are used widely for reaching different purposes, as remote access to information is very convenient. However, the remote access brings many aspects which should be handled. Users expect predictable performance levels (e.g., acceptable response time), therefore, service providers should know how their system performs under different loading conditions. In this thesis I design an analytical performance model and develop a tool which can solve that model. The tool allows analyzing the performance of web applications and answer the following questions: 1)What is the average response time of the system? 2)What is the utilization of the system as a whole? The input parameters, such as the average service time of transactions, average arrival rate of requests, and the average think time, are estimated from a real workload (of a system under test). The performance model is developed by means of Queuing Networks, a framework which enables the analysis of a system in terms of mathematical formula

A General Buffer Scheme for the Windows Scheduling Problem

Broadcasting is an efficient alternative to unicast for delivering popular on-demand media requests. Broadcasting schemes that are based on windows scheduling algorithms provide a way to satisfy all requests with both low bandwidth and low latency. Consider a system of n pages that need to be scheduled (transmitted) on identical channels an infinite number of times. Time is slotted, and it takes one time slot to transmit each page. In the windows scheduling problem (WS) each page i, 1 ≤ i ≤ n, is associated with a request window wi. In a feasible schedule for WS, page i must be scheduled at least once in any window of wi time slots. The objective function is to minimize the number of channels required to schedule all the pages. The main contribution of this paper is the design of a general buffer scheme for the windows scheduling problem such that any algorithm for WS follows this scheme. As a result, this scheme can serve as a tool to analyze and/or exhaust all possible WS-algorithms. The buffer scheme is based on modelling the system as a nondeterministic finite state machine in which any directed cycle corresponds to a legal schedule and vice-versa. Since WS is NP-hard, w

Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented