79 research outputs found
Modulated Branching Processes, Origins of Power Laws and Queueing Duality
Power law distributions have been repeatedly observed in a wide variety of
socioeconomic, biological and technological areas. In many of the observations,
e.g., city populations and sizes of living organisms, the objects of interest
evolve due to the replication of their many independent components, e.g.,
births-deaths of individuals and replications of cells. Furthermore, the rates
of the replication are often controlled by exogenous parameters causing periods
of expansion and contraction, e.g., baby booms and busts, economic booms and
recessions, etc. In addition, the sizes of these objects often have reflective
lower boundaries, e.g., cities do not fall bellow a certain size, low income
individuals are subsidized by the government, companies are protected by
bankruptcy laws, etc.
Hence, it is natural to propose reflected modulated branching processes as
generic models for many of the preceding observations. Indeed, our main results
show that the proposed mathematical models result in power law distributions
under quite general polynomial Gartner-Ellis conditions, the generality of
which could explain the ubiquitous nature of power law distributions. In
addition, on a logarithmic scale, we establish an asymptotic equivalence
between the reflected branching processes and the corresponding multiplicative
ones. The latter, as recognized by Goldie (1991), is known to be dual to
queueing/additive processes. We emphasize this duality further in the
generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection
4.
Information Ranking and Power Laws on Trees
We study the situations when the solution to a weighted stochastic recursion
has a power law tail. To this end, we develop two complementary approaches, the
first one extends Goldie's (1991) implicit renewal theorem to cover recursions
on trees; and the second one is based on a direct sample path large deviations
analysis of weighted recursive random sums. We believe that these methods may
be of independent interest in the analysis of more general weighted branching
processes as well as in the analysis of algorithms
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
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Heavy Tails and Instabilities in Large-Scale Systems with Failures
Modern engineering systems, e.g., wireless communication networks, distributed computing systems, etc., are characterized by high variability and susceptibility to failures. Failure recovery is required to guarantee the successful operation of these systems. One straight- forward and widely used mechanism is to restart the interrupted jobs from the beginning after a failure occurs. In network design, retransmissions are the primary building blocks of the network architecture that guarantee data delivery in the presence of channel failures. Retransmissions have recently been identified as a new origin of power laws in modern information networks. In particular, it was discovered that retransmissions give rise to long tails (delays) and possibly zero throughput. To this end, we investigate the impact of the âretransmission phenomenonâ on the performance of failure prone systems and propose adaptive solutions to address emerging instabilities.
The preceding finding of power law phenomena due to retransmissions holds under the assumption that data sizes have infinite support. In practice, however, data sizes are upper bounded 0 †L †b, e.g., WaveLANâs maximum transfer unit is 1500 bytes, YouTube videos are of limited duration, e-mail attachments cannot exceed 10MB, etc. To this end, we first provide a uniform characterization of the entire body of the distribution of the number of retransmissions, which can be represented as a product of a power law and the Gamma distribution. This rigorous approximation clearly demonstrates the transition from power law distributions in the main body to exponential tails. Furthermore, the results highlight the importance of wisely determining the size of data fragments in order to accommodate the performance needs in these systems as well as provide the appropriate tools for this fragmentation.
Second, we extend the analysis to the practically important case of correlated channels using modulated processes, e.g., Markov modulated, to capture the underlying dependencies. Our study shows that the tails of the retransmission and delay distributions are asymptotically insensitive to the channel correlations and are determined by the state that generates the lightest tail in the independent channel case. This insight is beneficial both for capacity planning and channel modeling since the independent model is sufficient and the correlation details do not matter. However, the preceding finding may be overly optimistic when the best state is atypical, since the effects of âbadâ states may still downgrade the performance.
Third, we examine the effects of scheduling policies in queueing systems with failures and restarts. Fair sharing, e.g., processor sharing (PS), is a widely accepted approach to resource allocation among multiple users. We revisit the well-studied M/G/1 PS queue with a new focus on server failures and restarts. Interestingly, we discover a new phenomenon showing that PS-based scheduling induces complete instability in the presence of retransmissions, regardless of how low the traffic load may be. This novel phenomenon occurs even when the job sizes are bounded/fragmented, e.g., deterministic. This work demonstrates that scheduling one job at a time, such as first-come-first-serve, achieves a larger stability region and should be preferred in these systems.
Last, we delve into the area of distributed computing and study the effects of commonly used mechanisms, i.e., restarts, fragmentation, replication, especially in cloud computing services. We evaluate the efficiency of these techniques under different assumptions on the data streams and discuss the corresponding optimization problem. These findings are useful for optimal resource allocation and fault tolerance in rapidly developing computing networks. In addition to networking and distributed computing systems, the aforementioned results improve our understanding of failure recovery management in large manufacturing and service systems, e.g., call centers. Scalable solutions to this problem increase in significance as these systems continuously grow in scale and complexity. The new phenomena and the techniques developed herein provide new insights in the areas of parallel computing, probability and statistics, as well as financial engineering
Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems
This open access book coherently gathers well-founded information on the fundamentals of and formalisms for modelling cyber-physical systems (CPS). Highlighting the cross-disciplinary nature of CPS modelling, it also serves as a bridge for anyone entering CPS from related areas of computer science or engineering. Truly complex, engineered systemsâknown as cyber-physical systemsâthat integrate physical, software, and network aspects are now on the rise. However, there is no unifying theory nor systematic design methods, techniques or tools for these systems. Individual (mechanical, electrical, network or software) engineering disciplines only offer partial solutions. A technique known as Multi-Paradigm Modelling has recently emerged suggesting to model every part and aspect of a system explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s), and then weaving the results together to form a representation of the system. If properly applied, it enables, among other global aspects, performance analysis, exhaustive simulation, and verification. This book is the first systematic attempt to bring together these formalisms for anyone starting in the field of CPS who seeks solid modelling foundations and a comprehensive introduction to the distinct existing techniques that are multi-paradigmatic. Though chiefly intended for master and post-graduate level students in computer science and engineering, it can also be used as a reference text for practitioners
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
Solving Multi-objective Integer Programs using Convex Preference Cones
Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron vĂctimas de algĂșn tipo de delito y la manera en que ocurriĂł el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en MĂ©xic
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