[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 1069884 |
Zbl 0696.60087
[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 0440729 |
Zbl 0342.60065
[5] X. R. Cao:
Convergence of parameter sensitivity estimates in a stochastic experiment. IEEE Trans. Automat. Control 30 (1985), 834-843.
MR 0799478 |
Zbl 0574.62081
[6] X. R. Cao:
First-order perturbation analysis of a single multi-class finite source queue. Performance Evaluation 7 (1987), 31-41.
MR 0882859
[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 0909965
[8] Y. C. Ho, C. Cassandras:
Infinitesimal and finite perturbation analysis for queueing networks. Automatica 19 (1983), 4, 439-445.
Zbl 0514.90028
[9] Y. C. Ho, S. Li:
Extensions of infinitesimal perturbation analysis. IEEE Trans. Automat. Control 33 (1988), 427-438.
MR 0936266 |
Zbl 0637.90091
[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 0820735
[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 0586154 |
Zbl 0498.60071
[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 0963167 |
Zbl 0643.60057
[14] R. Schassberger:
The intensitity of stationary probabilities in networks of queues. Adv. in Appl. Probab. 10 (1987), 906-912.
MR 0509223
[15] P. J. Schweitzer:
Perturbation theory and finite Markov chains. J. Appl. Probab. 5 (1968), 401-413.
MR 0234527
[16] E. Seneta:
Finite approximations to finite non-negative matrices. Cambridge Stud. Philos. 63 (1967), 983-992.
MR 0217874
[17] E. Seneta:
The principles of truncations in applied probability. Comment. Math. Univ. Carolin. 9 (1968), 533-539.
MR 0235640
[18] E. Seneta:
Non-Negative Matrices and Markov Chains. Springer Verlag, New York 1980.
MR 2209438
[19] J. G. Shantikumar, D. D. Yao:
Stochastic monotonicity of the queue lengths in closed queueing networks. Oper. Res. 35 (1987), 583-588.
MR 0924950
[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 0974496
[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 0754339 |
Zbl 0536.60085
[23] R. Suri:
A concept of monotonicity and its characterization for closed queueing networks. Oper. Res. 55 (1985), 606-024.
MR 0791711 |
Zbl 0567.90040
[24] R. Suri:
Infinitesimal perturbation analysis for general discrete event systems. J. Assoc. Comput. Mach. 31, (1987), 3, 686-717.
MR 0904200
[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 0847718
[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 0932536
[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 0938482 |
Zbl 0698.90034
[32] N. M. van Dijk:
A simple throughput bound for large closed queueing networks with finite capacities. Performance Evaluation 10 (1988), 153-167.
MR 1032181
[33] N. M. van Dijk:
A note on extended uniformization for non-exponential stochastic networks. J. Appl. Probab. 28 (1991), 955-961.
MR 1133809 |
Zbl 0746.60088
[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 0955756
[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 0932535
[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 0980419
[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 0595895 |
Zbl 0449.60064
[39] W. Whitt:
Stochastic comparison for non-Markov processes. Math. Oper. Res. 11 (1986), 4, 608-618.
MR 0865555
[40] P. Whittle:
Partial balance and insensitivity. Adv. in Appl. Probab. 22 (1985), 168-175.
MR 0776896 |
Zbl 0561.60095