Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-21T22:14:02.054Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Time Monotonicity for Performability Models

Published online by Cambridge University Press:  27 July 2009

Nico M. Van Dijk
Nico M. Van Dijk
Affiliation:
Faculty of Economic Sciences and Econometrics, University of Amsterdam, Roetersstraat 18, 1018 WB Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Extract

For a class of performability models with component-interdependent repairs and breakdowns, monotonicity is shown over time for expected availability measures. This result is of interest to justify steady-state bounds.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 299 - 310
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Adan, I.J.B.F. & Van der Wal, J. (1989). Monotonicity of the throughput of a closed queueing network in the number of jobs. Operations Research 37: 935–957.CrossRefGoogle Scholar
2.Adan, I.J.B.F. & Van der Wal, J. (1989). Monotonicity of the throughput in single server production and assembly networks with respect to buffer sizes. In Altiok, T. & Perros, H. (eds.), Queueing networks with blocking. North-Holland, pp. 345–356.Google Scholar
3.Keilson, J. & Kester, A. (1977). Monotone matrices and monotone Markov processes. Stochastic Processes and Their Applications 5: 231–241.CrossRefGoogle Scholar
4.Massey, W.A. (1987). Stochastic orderings for Markov processes on partially ordered spaces. Mathematics of Operations Research 12: 350–367.CrossRefGoogle Scholar
5.Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco: Holden-Day.Google Scholar
6.Shanthikumar, J.G. & Yao, D.D. (1987). General queueing networks: Representation and stochasticity. Proceedings of the 26th IEEE Conference on Decision and Control, pp. 1084–1087.CrossRefGoogle Scholar
7.Shanthikumar, J.G. & Yao, D.D. (1988). Monotonicity properties in cyclic queueing networks with finite buffers. In Altiok, T. & Perros, H. (eds.), Queueing networks with blocking. North-Holland, pp. 325–344.Google Scholar
8.Shanthikumar, J.G. & Yao, D.D. (1988). Throughput bounds for closed queuing networks with queue-independent service rates. Performance Evaluation 9: 69–78.CrossRefGoogle Scholar
9.Smeitink, E., van Dijk, N.M.,& Haverkort, B.R. (1992). Product forms for availability models. Applied Stochastic Models and Data Analysis 8: 283–302.CrossRefGoogle Scholar
10.Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
11.Tsoucas, P. & Walrand, J. (1989). Monotonicity of throughput in non-Markovian networks. Journal of Applied Probability 26: 134–141.CrossRefGoogle Scholar
12.van Dijk, N.M. & Puterman, M.L. (19xx). Perturbation theory for Markov reward processes with applications to queueing systems. Advances in Applied Probability 20: 79–89.CrossRefGoogle Scholar
13.van Dijk, N.M., Tsoucas, P., & Walrand, J. (1988). Simple bounds and monotonicity of the call congestion of infinite multiserver delay systems. Probability in the Engineering and Informational Sciences 2: 129–138.CrossRefGoogle Scholar
14.Whitt, W. (1981). Comparing counting processes and queues. Advances in Applied Probability 13: 207–220.CrossRefGoogle Scholar
15.Whitt, W. (1986). Stochastic comparison for non-Markov processes. Mathematics of Operations Research 11(4): 608–618.CrossRefGoogle Scholar