منابع مشابه
Timetable Synthesis Using (max,+) Algebra
This paper deals with control of transportation systems. We propose an approach based on dioid theory to compute timetables of a transportation network. We generalize the problem by considering additional constraints for the control objective. Copyright c ©2006 IFAC
متن کاملRailway Timetable Stability Analysis Using Stochastic Max-Plus Linear Systems
Stability and robustness of a railway timetable are essential properties for punctual and reliable operations. Timetable performance evaluation is therefore an important aspect in the timetable design process. In particular, the stability and recoverability properties of a timetable with respect to daily process time variations must be well analysed. The timetable must be able to recover from p...
متن کاملMax-plus algebra
The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, ...
متن کاملMax-algebra: the linear algebra of combinatorics?
Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machinescheduling, information technology and ...
متن کاملLinear systems in (max,+) algebra
Proceedings of the 29th Conference on Decision and Control Honolulu, Dec. 1990 Abstract In this paper, we study the general system of linear equations in the algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the algebra in the sense that every nondegenerate system of li...
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ژورنال
عنوان ژورنال: IFAC Proceedings Volumes
سال: 2006
ISSN: 1474-6670
DOI: 10.3182/20060517-3-fr-2903.00201