Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

Here are two books on a topic new to Technometrics: statistical and mathematical demography. The first author of Applied Mathematical Demography wrote the first two editions of this book alone. The second edition was published in 1985. Professor Keyfritz noted in the Preface (p. vii) that at age 90 he had no interest in doing another edition; however, the publisher encouraged him to find a coauthor. The result is an additional focus for the book in the world of biology that makes it much more relevant for the sciences. The book is now part of the publisher’s series on Statistics for Biology and Health. Much of it, of course, focuses on the many aspects of human populations. The new material focuses on mature population models, the particular focus of the new author (see, e.g., Caswell 2000). As one might expect from a book that was originally written in the 1970s, it does not include a lot of information on statistical computing. The new book by Alho and Spencer is focused on putting a better emphasis on statistics in the discipline of demography (Preface, p. vii). It is part of the publisher’s Series in Statistics. The authors are both statisticians, so the focus is on statistics as used for demographic problems. The authors are targeting human applications, so their perspective on science does not extend any further than epidemiology. The book actually strikes a good balance between statistical tools and demographic applications. The authors use the first two chapters to teach statisticians about the concepts of demography. The next four chapters are very similar to the statistics content found in introductory books on survival analysis, such as the recent book by Kleinbaum and Klein (2005), reported by Ziegel (2006). The next three chapters are focused on various aspects of forecasting demographic rates. The book concludes with chapters focusing on three areas of applications: errors in census numbers, financial applications, and small-area estimates.

Univariate Discrete Distributions

Patient Flow: Reducing Delay in Healthcare Delivery

Thank you for reading principles of random walk. Maybe you have knowledge that, people have search hundreds times for their chosen novels like this principles of random walk, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some malicious virus inside their desktop computer. principles of random walk is available in our book collection an online access to it is set as public so you can get it instantly. Our digital library hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the principles of random walk is universally compatible with any devices to read.

Principles Of Random Walk

Multiserver queueing systems describe situations in which users require service from multiple parallel servers. Examples include check-in lines at airports, waiting rooms in hospitals, queues in contact centers, data buffers in wireless networks, and delayed service in cloud data centers. These are all situations with jobs (clients, patients, tasks) and servers (agents, beds, processors) that have large capacity levels, ranging from the order of tens (checkouts) to thousands (processors). This survey investigates how to design such systems to exploit resource pooling and economies-of-scale. In particular, we review the mathematics behind the quality- and efficiency-driven (QED) regime, which lets the system operate close to full utilization, while the number of servers grows simultaneously large and delays remain manageable. Aimed at a broad audience, we describe in detail the mathematical concepts for the basic Markovian many-server system, and we provide only sketches or references for more advanced settings related to, e.g., load balancing, overdispersion, parameter uncertainty, general service requirements, and queueing networks. While serving as a partial survey of a massive body of work, the tutorial is not meant to be exhaustive.

/pdf/economies-of-scale-in-many-server-queueing-systems-tutorial-9xwo31enli.pdf

Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of time. Furthermore, demand for blood is impatient, i.e., a demand for blood may be canceled if it cannot be satisfied soon enough. For a range of perishability functions and demand impatience functions, we derive the steady-state distributions of the amount of blood kept in storage, and of the amount of demand for blood (at any point in time, at most one of these quantities is positive). Under certain conditions we also obtain the fluid and diffusion limits of the blood inventory process, showing in particular that the diffusion limit process is an Ornstein-Uhlenbeck process.

/pdf/a-blood-bank-model-with-perishable-blood-and-demand-442lv4svks.pdf

A Blood Bank Model with Perishable Blood and Demand Impatience

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete-time stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic.

/pdf/robust-heavy-traffic-approximations-for-service-systems-3nu250f1hu.pdf

Robust heavy-traffic approximations for service systems facing overdispersed demand

We introduce a family of heavy-traffic regimes for large-scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to economies-of-scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a nonstandard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.

/pdf/novel-heavy-traffic-regimes-for-large-scale-service-systems-3vgs88ankk.pdf

Novel Heavy-Traffic Regimes for Large-Scale Service Systems

Stochastic service systems describe situations in which customers compete for service from scarce resources. Think of check-in lines at airports, waiting rooms in hospitals or queues in supermarkets, where the scarce resource is human manpower. Next to these traditional settings, resource sharing is also important in large-scale service systems such as the internet, wireless networks and cloud computing facilities. In these virtual environments, geographical conditions do not restrict the system size, paving the way for the emergence of large-scale resource sharing networks. This thesis investigates how to design large-scale systems in order to achieve the dual goal of operational efficiency and quality-of-service, by which we mean that the system is highly occupied and hence efficiently utilizes the expensive resources, while at the same time, the level of service, experienced by customers, remains high.

/pdf/asymptotic-dimensioning-of-stochastic-service-systems-2ar6lcen0t.pdf

Britt W. J. Mathijsen

Papers

Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

A Blood Bank Model with Perishable Blood and Demand Impatience

Robust heavy-traffic approximations for service systems facing overdispersed demand

Novel Heavy-Traffic Regimes for Large-Scale Service Systems

Asymptotic dimensioning of stochastic service systems