Michel Mandjes

Bio: Michel Mandjes is an academic researcher from University of Amsterdam. The author has contributed to research in topics: Queue & Queueing theory. The author has an hindex of 35, co-authored 493 publications receiving 5249 citations. Previous affiliations of Michel Mandjes include Eindhoven University of Technology & Centrum Wiskunde & Informatica.

Modeling of customer retrial phenomenon in cellular mobile networks

Abstract: In the planning of modern cellular mobile communication systems, the impact of customer behavior has to be carefully taken into account. Two models dealing with the call retrial phenomenon are presented. The first model considers a base station with a finite customer population and repeated attempts. A Markov chain modeling is proposed, and an efficient recursive solution of the state probabilities is presented. The second model focuses on the use of the guard channel concept to prioritize the handover traffic. Again, the retrial phenomenon plays an important role. The influence of the repeated attempt effect on the quality of service experienced by the mobile customers is discussed by means of numerical results.

Queues and Lévy Fluctuation Theory

Abstract: The book provides an extensive introduction to queueing models driven by Levy-processes as well as a systematic account of the literature on Levy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Levy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Levy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.

Large Deviations for Small Buffers: An Insensitivity Result

Abstract: This article focuses on a queue fed by a large number of “semi-Markov modulated fluid sources”, e.g., on/off sources with on and off-times that have general distributions. The asymptotic regime is considered in which the number of sources grows large, and the buffer and link rate are scaled accordingly. We aim at characterizing the exponential decay rate of the buffer overflow probability for the regime of small buffers. An insensitivity result is proven: the decay rate depends on the distributions of the on and off-times only through their means. The efficiency gain to be achieved by using small buffers is significant, as the decay rate grows fast: proportionally to the square root of the buffer size.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Convergence of probability measures

Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an