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On the modelling and management of traffic

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases are...

On the modelling and management of traffic

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases...

On the power of randomization for job shop scheduling with k -units length tasks

Tobias Mömke (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In the job shop scheduling problem k -units- J m , there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D . The contribution of this paper are the following results; (i) for d = o ( D ) jobs and every fixed k , the makespan of an optimal schedule is at most D + o ( D ) , which extends the result of [3] for k = 1 ; (ii) a randomized on-line approximation algorithm for k -units-...

On the power of randomization for job shop scheduling with k-units length tasks

Tobias Mömke (2008)

RAIRO - Theoretical Informatics and Applications

In the job shop scheduling problem k-units-Jm, there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D. The contribution of this paper are the following results; (i) for d = o ( D ) jobs and every fixed k, the makespan of an optimal schedule is at most D+ o(D), which extends the result of [3] for k=1; (ii) a randomized on-line approximation...

On the queue-size distribution in the multi-server system with bounded capacity and packet dropping

Oleg Tikhonenko, Wojciech M. Kempa (2013)

Kybernetika

A multi-server M / M / n -type queueing system with a bounded total volume and finite queue size is considered. An AQM algorithm with the “accepting” function is being used to control the arrival process of incoming packets. The stationary queue-size distribution and the loss probability are derived. Numerical examples illustrating theoretical results are attached as well.

On the rate of convergence to the neutral attractor of a family of one-dimensional maps

T. Nowicki, M. Sviridenko, G. Świrszcz, S. Winograd (2009)

Fundamenta Mathematicae

For a family of maps f d ( p ) = 1 - ( 1 - p / d ) d , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

On the weak robustness of fuzzy matrices

Ján Plavka (2013)

Kybernetika

A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k ⊗ x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

On transient queue-size distribution in the batch-arrivals system with a single vacation policy

Wojciech M. Kempa (2014)

Kybernetika

A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of...

On transitive orientations of G-ê

Michael Andresen (2009)

Discussiones Mathematicae Graph Theory

A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.

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