Cycle time of stochastic event graphs: evaluation and marking optimization

1994 ◽  
Vol 39 (7) ◽  
pp. 1482-1486 ◽  
Author(s):  
J.-M. Proth ◽  
Xiao-Lan Xie
Keyword(s):  
Cycle Time ◽  
Stochastic Event Graphs ◽  
Stochastic Event

Products of Irreducible Random Matrices in the (Max, +) Algebra

1997 ◽  
Vol 29 (02) ◽  
pp. 444-477 ◽  
Author(s):  
Jean Mairesse
Keyword(s):  
Stationary Regime ◽  
Recursive Equation ◽  
Periodic Regime ◽  
Jackson Networks ◽  
Matrix Vector Multiplication ◽  
The Matrix ◽  
Max Algebra ◽  
Matrix Vector ◽  
Stochastic Event Graphs ◽  
Stochastic Event

We consider the recursive equation x(n + 1)= A(n)⊗x(n), where x(n + 1) and x(n) are ℝ k -valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj (Aij (n) + xj (n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence {A(n), n ∈ ℕ} is i.i.d. or, more generally, stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matrices such that and the matrices have a unique periodic regime.

scholarly journals Products of Irreducible Random Matrices in the (Max, +) Algebra

1997 ◽  
Vol 29 (2) ◽  
pp. 444-477 ◽  
Author(s):  
Jean Mairesse
Keyword(s):  
Stationary Regime ◽  
Recursive Equation ◽  
Periodic Regime ◽  
Jackson Networks ◽  
Matrix Vector Multiplication ◽  
The Matrix ◽  
Max Algebra ◽  
Matrix Vector ◽  
Stochastic Event Graphs ◽  
Stochastic Event

We consider the recursive equation x(n + 1)= A(n)⊗x(n), where x(n + 1) and x(n) are ℝk-valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj (Aij (n) + xj(n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the sequence {A(n), n ∈ ℕ} is i.i.d. or, more generally, stationary and ergodic. The main result of the paper states that the system couples in finite time with a unique stationary regime if and only if there exists a set of matrices such that and the matrices have a unique periodic regime.

scholarly journals Admission control in stochastic event graphs

2000 ◽  
Vol 45 (5) ◽  
pp. 854-867 ◽  
Author(s):  
E. Altman ◽  
B. Gaujal ◽  
A. Hordijk
Keyword(s):  
Admission Control ◽  
Stochastic Event Graphs ◽  
Stochastic Event
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