Queueing models for cable access networks

abstract in thesi

The W,ZW,Z scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends

First passage problems for spectrally negative L\'evy processes with possible absorbtion or/and reflection at boundaries have been widely applied in mathematical finance, risk, queueing, and inventory/storage theory. Historically, such problems were tackled by taking Laplace transform of the associated Kolmogorov integro-differential equations involving the generator operator. In the last years there appeared an alternative approach based on the solution of two fundamental "two-sided exit" problems from an interval (TSE). A spectrally one-sided process will exit smoothly on one side on an interval, and the solution is simply expressed in terms of a "scale function" $W$ (Bertoin 1997). The non-smooth two-sided exit (or ruin) problem suggests introducing a second scale function $Z$ (Avram, Kyprianou and Pistorius 2004). Since many other problems can be reduced to TSE, researchers produced in the last years a kit of formulas expressed in terms of the "$W,Z$ alphabet" for a great variety of first passage problems. We collect here our favorite recipes from this kit, including a recent one (94) which generalizes the classic De Finetti dividend problem. One interesting use of the kit is for recognizing relationships between apparently unrelated problems -- see Lemma 3. Last but not least, it turned out recently that once the classic $W,Z$ are replaced with appropriate generalizations, the classic formulas for (absorbed/ reflected) L\'evy processes continue to hold for: a) spectrally negative Markov additive processes (Ivanovs and Palmowski 2012), b) spectrally negative L\'evy processes with Poissonian Parisian absorbtion or/and reflection (Avram, Perez and Yamazaki 2017, Avram Zhou 2017), or with Omega killing (Li and Palmowski 2017)

Asymptotic performance of queue length based network control policies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 199-204).In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length information to perform effectively, which inevitably adds to the control overheads in a network. Therefore, it is important to understand the role played by queue length information in network control, and its impact on various performance metrics. In this thesis, we study the interplay between the asymptotic behavior of buffer occupancy, queue length information, and traffic statistics in the context of scheduling, flow control, and resource allocation. First, we consider a single-server queue and deal with the question of how often control messages need to be sent in order to effectively control congestion in the queue. Our results show that arbitrarily infrequent queue length information is sufficient to ensure optimal asymptotic decay for the congestion probability, as long as the control information is accurately received. However, if the control messages are subject to errors, the congestion probability can increase drastically, even if the control messages are transmitted often. Next, we consider a system of parallel queues sharing a server, and fed by a statistically homogeneous traffic pattern. We obtain the large deviation exponent of the buffer overflow probability under the well known max-weight scheduling policy. We also show that the queue length based max-weight scheduling outperforms some well known queue-blind policies in terms of the buffer overflow probability. Finally, we study the asymptotic behavior of the queue length distributions when a mix of heavy-tailed and light-tailed traffic flows feeds a system of parallel queues. We obtain an exact asymptotic queue length characterization under generalized max-weight scheduling. In contrast to the statistically homogeneous traffic scenario, we show that max-weight scheduling leads to poor asymptotic behavior for the light-tailed traffic, whereas a queue-blind priority policy gives good asymptotic behavior.by Krishna Prasanna Jagannathan.Ph.D

On the distribution of throughput of transfer lines

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 86-107A transfer line corresponds to a manufacturing system consisting of a number of work stations in series integrated into one system by a common transfer mechanism and a control system. There is a vast literature on the transfer lines. However, little has been done on the transient analysis of these systems by making use of the higher order moments of their performance measures due to the difficulty in determining the evolution of the stochastic processes under consideration. This thesis examines the transient behavior of relatively short transfer lines and derives the distribution of the performance measures of interest. The proposed method based on the analytical derivation of the distribution of throughput is also applied to the systems with two-part types. An experiment is designed in order to compare the results of this study with the state-space representations and the simulation. They are also interpreted from the point of view of the line behavior and design issue. Furthermore, extensions are briefly discussed and directions for future research are suggested.Deler, BaharM.S

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes