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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...

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