Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Aquatic plants convert mean kinetic energy into turbulent kinetic energy at the scale of the plant stems and branches. This energy transfer, linked to wake generation, affects vegetative drag and turbulence intensity. Drawing on this physical link, a model is developed to describe the drag, turbulence and diffusion for flow through emergent vegetation which for the first time captures the relevant underlying physics, and covers the natural range of vegetation density and stem Reynolds' numbers. The model is supported by laboratory and field observations. In addition, this work extends the cylinder-based model for vegetative resistance by including the dependence of the drag coefficient, CD, on the stem population density, and introduces the importance of mechanical diffusion in vegetated flows.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998WR900069

Drag, turbulence, and diffusion in flow through emergent vegetation

Loading estimates of lead, copper, cadmium, and zinc in urban runoff from specific sources

Storm water runoff from urban roadways often contains significant quantities of metal elements and solids. These anthropogenic constituents are generated mainly from traffic-related activities. Metal elements partition into dissolved and particulate-bound fractions as a function of pH, pavement residence time, and solids concentration. Lateral pavement sheet flow from an experimental field site on a heavily traveled urban highway in Cincinnati was sampled during five rainfall runoff events in 1995. Results indicate that Zn, Cd, and Cu are mainly in dissolved form while Pb, Fe, and Al are mainly particulate-bound. Dissolved fractions of Zn, Cd, and Cu exhibited a strong first flush in lateral pavement sheet flow. Pb exhibited a weak first flush for all events. Event mean concentrations of Zn, Cd, and Cu exceed surface water quality discharge standards. Findings from this study will assist in the development of effective control strategies for the immobilization of metal elements and solids in urban runoff.

Partitioning and first flush of metals in urban roadway storm water

Residential End Uses of Water

Urban stormwater runoff from paved surfaces transports a wide gradation of solids ranging in size from smaller than 1 micrometer to greater than 10,000 micrometers. This study measured physical characteristics of solids transported in lateral pavement sheet flow (LPSF) from a heavily traveled roadway in Cincinnati, Ohio. Particles smaller than 25 micrometers were counted and sized using a light obscuration particle counter. Particles larger than 25 micrometers were separated mechanically to generate particle size distributions. Solids in the 2-8 micrometer range generated the largest counts and were rapidly washed from the pavement. LPSF rate and duration controlled yield and size of transported solids. Particle transport was mass limited during long duration high intensity events, but flow limited during intermittent low intensity events with high traffic. Particle counts exhibited a first flush from the pavement. Specific surface area generally increased with decreasing particle size, but measured values deviated from the monotonic pattern expected for spherical particles. Particles 425-850 micrometers in size contributed the greatest total surface area. Results provide guidance for assessment of the impact of urban runoff water quality and for design of in situ treatment strategies.

Physical characteristics of urban roadway solids transported during rain events

Characterization of solid and metal element distributions in urban highway stormwater

Residential water use is visualized as a customer-server interaction often encountered in queueing theory. Individual customers are assumed to arrive according to a nonhomogeneous Poisson process, then engage water servers fro random lengths of time. Busy servers are assumed to draw water at steady but random rates from the distribution system. These conditions give rise to a time-dependent Markovian queueing system having servers that deliver random rectangular pulses of water. Expressions are derived for the mean, variance, and probability distribution of the flow rate and the corresponding pipe Reynolds number at points along a dead-end trunk line. Comparison against computer-simulated results shows that the queueing model provides an excellent description of the temporal and spatial variations of the flow regime through a dead-end trunk line supplying water to a block of heterogeneous homes. The behavior of the local flow field given by the queueing model can be coupled with water-quality models that require ultra-fine temporal and spatial resolutions to predict the fate of contaminants moving through municipal distribution systems.

Model for Instantaneous Residential Water Demands

Water demands at four single-family residences were monitored for a 1-yr period. About 8,000 demands per capita were recorded and converted to single equivalent rectangular pulses. Each pulse was classified by type (deterministic or random), location (indoor or outdoor) and day (weekday or weekend). Basic exploratory data analyses were performed to estimate sample statistics, cumulative distributions, and hourly occurrences of the intensity, duration, and volumes of the rectangular pulses according to type, location, and day. In addition, the hypothesis that residential water demands occur as a nonhomogeneous Poisson rectangular pulse process was examined. Results show that the simple rectangular pulse provided a very reasonable approximation of indoor water demands. However, the variance of the daily pulse count appears to be too high for Poisson process. Potential causes of the high variance in the daily pulse count are discussed. Findings and data from this study can be used to develop and verify fine-resolution network models designed to predict the fate and travel time distribution of substances moving to remote points of consumption in the water distribution system.

Steven G. Buchberger

Papers

Partitioning and first flush of metals in urban roadway storm water

Physical characteristics of urban roadway solids transported during rain events

Characterization of solid and metal element distributions in urban highway stormwater

Model for Instantaneous Residential Water Demands

Intensity, Duration, and Frequency of Residential Water Demands