On the estimation of the throughput for a class of stochastic resources sharing systems

Mathematics of Operations Research

Volumn 23, Issue 2, 1998, Pages 305-321

  Brilman, Matthieu ^a   Vincent, Jean Marc ^a  

^a IMAG CNRS   (France)

Author keywords

(max, +) systems; Parallel systems; Shared resources; Stochastic processes; Synchronization

Indexed keywords

DATA COMMUNICATION SYSTEMS; GRAPH THEORY; PARAMETER ESTIMATION; PERFORMANCE; RANDOM PROCESSES; SYNCHRONIZATION;

BOUNDS; STOCHASTIC RESOURCES SHARING SYSTEMS; THROUGHPUT ESTIMATION;

MATHEMATICAL MODELS;

EID: 0032069435     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.23.2.305     Document Type: Article

References (19)

1. Baccelli, F., P. Konstanpopoulos (1991). Estimates of cycle time in stochastic Petri nets, I. Karatzas, ed., Proceedings of Workshop on Stochastic Analysis, Springer-Verlag, Rutgers University.
2. _, Z. Liu (1991). Comparaison properties of stochastic decision free Petri nets. IEEE Trans. Automat. Control 37 (12), 1905-1992.
3. _, G. Cohen, G. Olsder, J.-P. Quadrat (1992). Synchronization and Linearity : An Algebra for Discrete Event Systems. John Wiley and Sons, New York.
4. Barbosa, V. C., E. Gafni (1989). Concurrency in heavily loaded neighborhood-constrained systems. ACM Trans. Prog. Lang, and Syst. 11 (4), 562-584.
5. Brilman, M. (1996). Modélisation et évaluation de performances de systèmes de ressources partagées, Thèse, Université Joseph Fourier, Grenoble.
6. _, J.-M. Vincent (1997). Synchronization by resource sharing: A performance analysis. Stochastic Models 13(3), 605-619.
7. Chandy, K., J. Misra (1984). The drinking philosopher's problem. ACM Trans. Prog. Long, and Syst. 6(4), 632-646.
8. Conway, A. (1989). Product-form and intensitivity in circuit-switched networks with failing links. Performance Evaluation 9(3), 209-215.
9. Gantmacher, F. (1960). The Theory of Matrices, Chelsea Publishing Company.
10. Glasserman, P., D. Yao (1995). Stochastic vector difference equations with stationary coefficients. J. Appl. Probab. 32(4). 851-866.
11. Golub, G , C. Van Loan (1987). Matrix Computations. Hopkins University Press.
12. Grötschel, M., L. Lovász, A. Schrijver (1981). The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (2), 169-197.
13. Kelly, F. (1991). Loss networks. Ann. Appl. Probab. 1 (3), 319-378.
14. Mairesse, J. (1997). Products of irreducible random matrices in the (Max, +) algebra-part 1. Adv. in Appl. Probab. 29 (2), 444-477.
15. Mitra, D. (1985). Probabilistic models and asymptotic results for concurrent processing with exclusive and non-exclusive locks. SIAM J. Comput. 14(4). 1030-1051.
16. _, P. Weinberger (1984). Probabilistic models of database locking: Solutions computational algorithms, and asymptotics. J. Assoc. Comput. Mach. 31 (4), 855-878.
17. Stahl, S. (1976). n-tuple colorings and associated graphs. J. Combin. Theory Ser. B 20(2), 185-203.
18. Vincent, J.-M. (1997a). On the (max, +)-structure of reservation systems, in European Control Conference, Brussels.
19. _ (1997b). Some ergodic results on stochastic iterative discrete event systems. Discrete Event Dynamic Syst. 7 (2), 209-232.