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

A note on stable flow-equivalent aggregation in closed networks

Samhället har tagit på sig ett stort ansvar för de barn som placeras utanför hemmet. Många av dem har upplevt svårigheter och inte fått tillräcklig omvårdnad. Ska dessa barn få samma möjlighet till ett gott liv som sina jämnåriga kamrater behöver de därför ett minst lika bra omhändertagande, av både fosterföräldrar och samhället i stort. Barn som lever i fosterhem är en mycket heterogen grupp. De behöver olika vård och bemötande i familjehemmet för att utvecklas optimalt. Just detta mycket komplexa förhållande berörs inte i denna kunskapsöversikt. Här har vi valt att fokusera på samhällets grundläggande omhändertagande av barnen. Tre primära beståndsdelar i den nordiska välfärdsmodellen är att ge barn en god och jämlik utbildning, förebygga hälsoproblem och underlätta övergången från barndom till vuxenliv. Det är dessa områden som beskrivs här. Den nordiska forskning som finns pekar på att barn som växer upp i fosterhem inte får samma goda stöd som andra barn på dessa områden och det tycks inte bli bättre under tiden i vård! Nordens Välfärdscenter och författarna presenterar konkreta rekommendationer om hur man kan förbättra situationen för fosterhemsplacerade barn. Det är rekommendationer som sannolikt förhindrar utanförskap och ohälsa för ett antal av dem på både kort och lång sikt.Nordens Barn - Fokus på barn i fosterhe

A diffusion model of scheduling control in queueing systems with many servers

This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers working in parallel, grouped in several stations. Servers in different stations offer service to customers of each class at possibly different rates. The control corresponds to selecting what customer class each server serves at each time. The diffusion control problem does not seem to have explicit solutions and therefore a characterization of optimal solutions via the Hamilton-Jacobi-Bellman equation is addressed. Our main result is the existence and uniqueness of solutions of the equation. Since the model is set on an unbounded domain and the cost per unit time is unbounded, the analysis requires estimates on the state process that are subexponential in the time variable. In establishing these estimates, a key role is played by an integral formula that relates queue length and idle time processes, which may be of independent interest.Comment: Published at http://dx.doi.org/10.1214/105051604000000963 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

QMLE: a methodology for statistical inference of service demands from queueing data

Estimating the demands placed by services on physical resources is an essential step for the definition of performance models. For example, scalability analysis relies on these parameters to predict queueing delays under increasing loads. In this paper, we investigate maximum likelihood (ML) estimators for demands at load-independent and load-dependent resources in systems with parallelism constraints. We define a likelihood function based on state measurements and derive necessary conditions for its maximization. We then obtain novel estimators that accurately and inexpensively obtain service demands using only aggregate state data. With our approach, and also thanks to approximation methods for computing marginal and joint distributions for the load-dependent case, confidence intervals can be rigorously derived, explicitly taking into account both topology and concurrency levels of the services. Our estimators and their confidence intervals are validated against simulations and real system measurements for two multi-tier applications, showing high accuracy also in the presence of load-dependent resources

Dynamic Time Windows and Generalized Virtual Clocks-Combined Closed-Loop/Open-Loop Mechanisms for Congestion Control of Data Traffic in High Speed Wide Area Networks

This paper presents a set of mechanisms for congestion control of data traffic in high speed wide area networks (HSWANs) along with preliminary performance results. The model of the network assumes reservation of resources based on average requirements. The mechanisms address (a) the different network time constants (short term and medium-term), (b) admission control that allows controlled variance of traffic as a function of medium-term congestion, and (c) prioritized scheduling which is based on a new fairness criterion. This latter criterion is perceived as the appropriate fairness measure for HSWANs. Preliminary performance studies show that the queue length statistics at switching nodes (mean, variance and max) are approximately proportional to the end-point \u27time window\u27 size. Further, * when network utilization approaches unity, the time window mechanism can protect the network from buffer overruns and excessive queueing delays, and * when network utilization level is smaller, the time window may be increased to allow a controlled amount of variance that attempts to simultaneously meet the performance goals of the end-user and that of the network. The prioritized scheduling algorithms proposed and studied in this paper are a generalization of the Virtual Clock algorithm [Zhang 1989]. The study here investigates * necessary and sufficient conditions for accomplishing desired fairness, * simulation and (limited analytical results for expected waiting times, * ability to protect against misbehaving users, and * relationship between end-point admission control (Time-Window) and internal scheduling (\u27Pulse\u27 and Virtual Clock) at the switch