Sensitivity error bounds for non-exponential stochastic networks
Kybernetika, Tome 31 (1995) no. 2, pp. 175-188 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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     title = {Sensitivity error bounds for non-exponential stochastic networks},
     journal = {Kybernetika},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1995_31_2_a3/}
}
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van Dijk, Nico M. Sensitivity error bounds for non-exponential stochastic networks. Kybernetika, Tome 31 (1995) no. 2, pp. 175-188. http://geodesic.mathdoc.fr/item/KYB_1995_31_2_a3/

[1] I. J. B. F. Adan, J. van der Wal: Monotonicity of the throughput of a closed queueing network in the number of jobs. Oper. Res. 57 (1989), 953-957. | MR | Zbl

[2] I. J. B. F. Adan, J. van der Wal: Monotonicity of the throughput in single server production and assembly networks with respect to the buffer sizes. In: Proceedings of the 1st International Workshop on Queueing Systems with Blocking. North-Holland 1989, pp. 345-356.

[3] A. D. Barbour: Networks of queues and the method of stages. Adv. in Appl. Probab. 8 (1976), 584-591. | MR | Zbl

[4] J. W. Cohen: Sensitivity and insensitivity. Delft Progr. Rep. 5 (1980), 159-173. | MR | Zbl

[5] X. R. Cao: Convergence of parameter sensitivity estimates in a stochastic experiment. IEEE Trans. Automat. Control 30 (1985), 834-843. | MR | Zbl

[6] X. R. Cao: First-order perturbation analysis of a single multi-class finite source queue. Performance Evaluation 7 (1987), 31-41. | MR

[7] X. R. Cao, Y. C. Ho: Sensitivity estimate and optimization of throughput in a production line with blocking. IEEE Trans. Automat. Control 32 (1987), 959-967. | MR

[8] Y. C. Ho, C. Cassandras: Infinitesimal and finite perturbation analysis for queueing networks. Automatica 19 (1983), 4, 439-445. | Zbl

[9] Y. C. Ho, S. Li: Extensions of infinitesimal perturbation analysis. IEEE Trans. Automat. Control 33 (1988), 427-438. | MR | Zbl

[10] P. Glasserman, Y. C. Ho: Aggregation approximations for sensitivity analysis of multi-class queueing networks. Performance Evaluation.

[11] A. Hordijk, N.M. van Dijk: Adjoint process, job-local balance and intensitivity of stochastic networks. Bull. 44th Session Int. Inst. 50 (1983), 776-788. | MR

[12] C. D. Meyer, Jr.: The condition of a finite Markov chain and perturbation bounds for the limiting probabilities. SIAM J. Algebraic Discrete Methods 1 (1980), 273-283. | MR | Zbl

[13] J. R. Rohlicek, A. S. Willsky: The reduction of perturbed Markov generators: an algorithm exposing the role of transient states. J. Assoc. Comput. Mach. 35 (1988), 675-696. | MR | Zbl

[14] R. Schassberger: The intensitity of stationary probabilities in networks of queues. Adv. in Appl. Probab. 10 (1987), 906-912. | MR

[15] P. J. Schweitzer: Perturbation theory and finite Markov chains. J. Appl. Probab. 5 (1968), 401-413. | MR

[16] E. Seneta: Finite approximations to finite non-negative matrices. Cambridge Stud. Philos. 63 (1967), 983-992. | MR

[17] E. Seneta: The principles of truncations in applied probability. Comment. Math. Univ. Carolin. 9 (1968), 533-539. | MR

[18] E. Seneta: Non-Negative Matrices and Markov Chains. Springer Verlag, New York 1980. | MR

[19] J. G. Shantikumar, D. D. Yao: Stochastic monotonicity of the queue lengths in closed queueing networks. Oper. Res. 35 (1987), 583-588. | MR

[20] J. G. Shantikumar, D. D. Yao: Throughput bounds for closed queueing networks with queue-dependent service rates. Performance Evaluation 9 (1987), 69-78. | MR

[21] J. G. Shantikumar, D. D. Yao: Monotonicity properties in cycbc queueing networks with finite buffers. In: Proceedings of the First Int. Workshop on Queueing Networks with Blocking. North Carolina 1988.

[22] D. Stoyan: Comparison Methods for Queues and Other Stochastic Models. J. Wiley, New. York 1983. | MR | Zbl

[23] R. Suri: A concept of monotonicity and its characterization for closed queueing networks. Oper. Res. 55 (1985), 606-024. | MR | Zbl

[24] R. Suri: Infinitesimal perturbation analysis for general discrete event systems. J. Assoc. Comput. Mach. 31, (1987), 3, 686-717. | MR

[25] R. Suri: Perturbation analysis. The state of the art and research issues explained via the GI/GI/1 queue. In: Proceedings of the IEEE.

[26] H. C. Tijms: Stochastic Modelling and Analysis. A Computational Approach. J. Wiley, New York 1986. | MR

[27] P. Tsoucas, J. Walrand: Monotonicity of throughput in non-markovian networks. J. Appl. Probab. (1983).

[28] N. M. van Dijk: A formal proof for the insensivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results. Stochastic Process. Appl. 27 (1988), 216-277.

[29] N. M. van Dijk: Perturbation theory for unbounded Markov reward process with applications to queueing. Adv. in Appl. Probab. 20 (1988), 99-111. | MR

[30] N. M. van Dijk: Simple performance bounds for non-product form queueing networks. In: Proceedings of the First International Workshop on Queueing Networks with Blocking. North-Holland 1988, pp. 1-18.

[31] N. M. van Dijk: Simple bounds for queueing systems with breakdowns. Performance Evaluation 7 (1988), 117-128. | MR | Zbl

[32] N. M. van Dijk: A simple throughput bound for large closed queueing networks with finite capacities. Performance Evaluation 10 (1988), 153-167. | MR

[33] N. M. van Dijk: A note on extended uniformization for non-exponential stochastic networks. J. Appl. Probab. 28 (1991), 955-961. | MR | Zbl

[34] N. M. van Dijk, B. F. Lamond: Bounds for the call congestion of finite single-server exponential tandem queues. Oper. Res. 36 (1988), 470-477. | MR

[35] N. M. van Dijk, M. L. Puterman: Perturbation theory for MarJcov reward processes with applications to queueing systems. Adv. in Appl. Probab. 20 (1988), 79-99. | MR

[36] N. M. van Dijk, J. van der Wal: Simple bounds and monotonicity results for multi-server exponential tandem queues. Queueing Systems Theory Appl. 4 (1989), 1-16. | MR

[37] E. W. B. van Marion: Influence of holding time distributions or blocking probabilities of a grading. TELE 20 (1968), 17-20.

[38] W. Whitt: Comparing counting processes and queues. Adv. in Appl. Probab. 13 (1981), 207-220. | MR | Zbl

[39] W. Whitt: Stochastic comparison for non-Markov processes. Math. Oper. Res. 11 (1986), 4, 608-618. | MR

[40] P. Whittle: Partial balance and insensitivity. Adv. in Appl. Probab. 22 (1985), 168-175. | MR | Zbl