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Nanonetworks: The graph theory framework for modeling nanoscale systems

Jelena Živkovic, Bosiljka Tadic (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked...

Nash equilibria for a model of traffic flow with several groups of drivers

Alberto Bressan, Ke Han (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κi drivers, sharing the same departure and arrival costs ϕi(t),ψi(t). For any given population sizes κ1,...,κn, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure...

New algorithms for coupled tasks scheduling – a survey

Jacek Blazewicz, Grzegorz Pawlak, Michal Tanas, Wojciech Wojciechowicz (2012)

RAIRO - Operations Research - Recherche Opérationnelle

The coupled tasks scheduling problem is a class of scheduling problems introduced for beam steering software of sophisticated radar devices, called phased arrays. Due to increasing popularity of such radars, the importance of coupled tasks scheduling is constantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, and only a few practically usable algorithms for such problems were found. This paper provides a survey of already known complexity results of various variants of...

New representation to reduce the search space for the resource-constrained project scheduling problem

Khaled Moumene, Jacques A. Ferland (2008)

RAIRO - Operations Research

This paper describes a new representation for the solutions of the resource-constrained project scheduling problem (RCPSP) denoted Activity Set List. The most efficient heuristics for the problem use the activity list representation and the serial SGS method to construct the corresponding solution (schedule). The activity list may induce a search space of representations much larger then the space of schedules because the same schedule can correspond to many different activity list representations....

Newsboy Problem: Viability of Optimal Initial Selling Price and Ordering Policies in the Presence of Exogenous Price Decline and Random Lead Time

Ningombam Sanjib Meitei, Snigdha Banerjee (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Analysis of empirical sales data lead us to consider newsboy model for four practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies are conducted to assess the effects of lead time and price...

Newsvendor solutions with general random yield distributions

Scott E. Grasman, Zaki Sari, Tewfik Sari (2007)

RAIRO - Operations Research

Most systems are characterized by uncertainties that cause throughput to be highly variable, for example, many modern production processes and services are substantially affected by random yields. When yield is random, not only is the usable quantity uncertain, but the random yield reduces usable capacity and throughput in the system. For these reasons, strategies are needed that incorporate random yield. This paper presents the analysis of the newsvendor model with a general random yield distribution,...

Node assignment problem in Bayesian networks

Joanna Polanska, Damian Borys, Andrzej Polanski (2006)

International Journal of Applied Mathematics and Computer Science

This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.

Nonlinear Markov processes in big networks

Quan-Lin Li (2016)

Special Matrices

Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Wojciech M. Kempa, Dariusz Kurzyk (2022)

Kybernetika

Non-stationary behavior of departure process in a finite-buffer M X / G / 1 / K -type queueing model with batch arrivals, in which a threshold-type waking up N -policy is implemented, is studied. According to this policy, after each idle time a new busy period is being started with the N th message occurrence, where the threshold value N is fixed. Using the analytical approach based on the idea of an embedded Markov chain, integral equations, continuous total probability law, renewal theory and linear algebra, a...

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